Equipment to study basic automotive electricity. Do not hesitate and contact us. Click on the button and ask for more information. We will answer you as soon as possible. Technical specifications. Circuit with lamps: Parallel, series, mixed, lamps with different powers. Circuit with resistances: Parallel, series, mixed, linear and logarithmic potentiometer. Circuit with relay. Circuits with capacitors: filter, power store. Circuit with logic gates. Test points to take measurements on the different circuits.

Accessibility to all components for analysis under voltage or without voltage. Antennas: Mono pole, horn, rhombic and parabolic reflector, array, and Yagi-Uda antenna. Light propagation through optical fiber: Ray optics theory and mode theory. Optical fiber: Types and characteristics, transmission characteristics, fiber joints and fiber couplers. Light sources: Light emitting diodes and laser diodes. Detectors: PIN photo-detector and avalanche photo-detectors.

Receiver analysis: Direct detection and coherent detection, noise and limitations. Transmission limitations: Chromatic dispersion, nonlinear refraction, four wave mixing and laser phase noises. Optical amplifier: Laser and fiber amplifiers, applications and limitations. Multi-channel optical system: Frequency division multiplexing, wavelength division multiplexing and co-channel interference.

Introduction: Communication channels, mathematical model and characteristics. Probability and stochastic processes. Source coding: Mathematical models of information, entropy, Huffman code and linear predictive coding. Digital transmission system: Base band digital transmission, inter-symbol interference, bandwidth, power efficiency, modulation and coding trade-off. Receiver for AWGN channels: Correlation demodulator, matched filter demodulator and maximum likelihood receiver.

Channel capacity and coding: Channel models and capacities and random selection of codes. Block codes and conventional codes: Linear block codes, convolution codes and coded modulation. Spread spectrum signals and system. Introduction: Concept, evolution and fundamentals. Analog and digital cellular systems. Cellular Radio System: Frequency reuse, co-channel interference, cell splitting and components.

Mobile radio propagation: Propagation characteristics, models for radio propagation, antenna at cell site and mobile antenna. Frequency Management and Channel Assignment: Fundamentals, spectrum utilization, fundamentals of channel assignment, fixed channel assignment, non-fixed channel assignment, traffic and channel assignment. Handoffs and Dropped Calls: Reasons and types, forced handoffs, mobile assisted handoffs and dropped call rate.

Diversity Techniques: Concept of diversity branch and signal paths, carrier to noise and carrier to interference ratio performance. Digital cellular systems: Global system for mobile, time division multiple access and code division multiple access. Introduction: Principle, evolution, networks, exchange and international regulatory bodies. Telephone apparatus: Microphone, speakers, ringer, pulse and tone dialing mechanism, side-tone mechanism, local and central batteries and advanced features.

Switching system: Introduction to analog system, digital switching systems - space division switching, blocking probability and multistage switching, time division switching and two dimensional switching. Traffic analysis: Traffic characterization, grades of service, network blocking probabilities, delay system and queuing. Modern telephone services and network: Internet telephony, facsimile, integrated services digital network, asynchronous transfer mode and intelligent networks.

Introduction to cellular telephony and satellite communication. Electronics Group. Review of FET amplifiers: Passive and active loads and frequency limitation. Current mirror: Basic, cascode and active current mirror. Differential Amplifier: Introduction, large and small signal analysis, common mode analysis and differential amplifier with active load. Noise: Introduction to noise, types, representation in circuits, noise in single stage and differential amplifiers and bandwidth.

Band-gap references: Supply voltage independent biasing, temperature independent biasing, proportional to absolute temperature current generation and constant transconductance biasing. Switch capacitor circuits: Sampling switches, switched capacitor circuits including unity gain buffer, amplifier and integrator. Substrate materials: Crystal growth and wafer preparation, epitaxial growth technique, molecular beam epitaxy, chemical vapor phase epitaxy and chemical vapor deposition CVD. Doping techniques: Diffusion and ion implantation. Etching: Wet chemical etching, silicon and GaAs etching, anisotropic etching, selective etching, dry physical etching, ion beam etching, sputtering etching and reactive ion etching.

Cleaning: Surface cleaning, organic cleaning and RCA cleaning. Lithography: Photo-reactive materials, pattern generation, pattern transfer and metalization.

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Discrete device fabrication: Diode, transistor, resistor and capacitor. Integrated circuit fabrication: Isolation - pn junction isolation, mesa isolation and oxide isolation. Testing, bonding and packaging. VLSI technology: Top down design approach, technology trends and design styles. CMOS circuit characteristics and performance estimation: Resistance, capacitance, rise and fall times, delay, gate transistor sizing and power consumption. CMOS circuit and logic design: Layout design rules and physical design of simple logic gates.

CMOS subsystem design: Adders, multiplier and memory system, arithmetic logic unit. Programmable logic arrays. VLSI testing. Compound semiconductor: Zinc-blend crystal structures, growth techniques, alloys, band gap, density of carriers in intrinsic and doped compound semiconductors. Hetero-Junctions: Band alignment, band offset, Anderson's rule, single and double sided hetero-junctions, quantum wells and quantization effects, lattice mismatch and strain and common hetero-structure material systems.

Hetero-Junction diode: Band banding, carrier transport and I-V characteristics. Hetero-junction field effect transistor: Structure and principle, band structure, carrier transport and I-V characteristics. Hetero-structure bipolar transistor HBT : Structure and operating principle, quasi-static analysis, extended Gummel-Poon model, Ebers-Moll model, secondary effects and band diagram of a graded alloy base HBT. VLSI MOS system design: Layout extraction and verification, full and semi-full custom design styles and logical and physical positioning.

Design entry tools: Schematic capture and HDL. Logic and switch level simulation. Static timing. Concepts and tools of analysis, solution techniques for floor planning, placement, global routing and detailed routing. Application specific integrated circuit design including FPGA.

Optical properties in semiconductor: Direct and indirect band-gap materials, radiative and non-radiative recombination, optical absorption, photo-generated excess carriers, minority carrier life time, luminescence and quantum efficiency in radiation. Properties of light: Particle and wave nature of light, polarization, interference, diffraction and blackbody radiation.

Light emitting diode LED : Principles, materials for visible and infrared LED, internal and external efficiency, loss mechanism, structure and coupling to optical fibers. Stimulated emission and light amplification: Spontaneous and stimulated emission, Einstein relations, population inversion, absorption of radiation, optical feedback and threshold conditions.

Semiconductor Lasers: Population inversion in degenerate semiconductors, laser cavity, operating wavelength, threshold current density, power output, hetero-junction lasers, optical and electrical confinement. Introduction to quantum well lasers. Photo-detectors: Photoconductors, junction photo-detectors, PIN detectors, avalanche photodiodes and phototransistors. Solar cells: Solar energy and spectrum, silicon and Schottkey solar cells. Modulation of light: Phase and amplitude modulation, electro-optic effect, acousto-optic effect and magneto-optic devices.

Introduction to integrated optics. Lattice vibration: Simple harmonic model, dispersion relation, acoustic and optical phonons. Band structure: Isotropic and anisotropic crystals, band diagrams and effective masses of different semiconductors and alloys. Scattering theory: Review of classical theory, Fermi-Golden rule, scattering rates of different processes, scattering mechanisms in different semiconductors, mobility. Different carrier transport models: Drift-diffusion theory, ambipolar transport, hydrodynamic model, Boltzman transport equations, quantum mechanical model, simple applications.

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Power Group. Transmission lines cables: overhead and underground. Stability: swing equation, power angle equation, equal area criterion, multi-machine system, step by step solution of swing equation. Factors affecting stability. Reactive power compensation. High voltage DC transmission system. Power quality: harmonics, sag and swell. Special machines: series universal motor, permanent magnet DC motor, unipolar and bipolar brush less DC motors, stepper motor and control circuits.

Reluctance and hysteresis motors with drive circuits, switched reluctance motor, electro static motor, repulsion motor, synchros and control transformers. Permanent magnet synchronous motors. Acyclic machines: Generators, conduction pump and induction pump. Magneto hydrodynamic generators. Fuel Cells, thermoelectric generators, flywheels. Vector control, linear motors and traction. Photovoltaic systems: stand alone and grid interfaced. Rectifiers: Uncontrolled and controlled single phase and three phase.

Regulated power supplies: Linear-series and shunt, switching buck, buckboost, boost and Cuk regulators. AC voltage controllers: single and three phase. DC motor control. Single phase cycloconverter. Inverters: Single phase and three phase voltage and current source. AC motor control. Stepper motor control. Resonance inverters. Pulse width modulation control of static converters. Power plants: general layout and principles, steam turbine, gas turbine, combined cycle gas turbine, hydro and nuclear.

Power plant instrumentation. Selection of location: Technical, economical and environmental factors. Load forecasting. Generation scheduling: deterministic and probabilistic. Electricity tariff: formulation and types. Purpose of power system protection. Criteria for detecting faults: over current, differential current, difference of phase angles, over and under voltages, power direction, symmetrical components of current and voltages, impedance, frequency and temperature.

Instrument transformers: CT and PT. Electromechanical, electronic and digital Relays: basic modules, over current, differential, distance and directional. Trip circuits. Unit protection schemes: Generator, transformer, motor, bus bar, transmission and distribution lines. Miniature circuit breakers and fuses. Circuit breakers: Principle of arc extinction, selection criteria and ratings of circuit breakers, types - air, oil, SF6 and vacuum.

Review of probability concepts. Probability distribution: Binomial, Poisson, and Normal. Reliability concepts: Failure rate, outage, mean time to failure, series and parallel systems and redundancy. Markov process.

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Probabilistic generation and load models. Reliability indices: Loss of load probability and loss of energy probability. Frequency and duration. Reliability evaluation techniques of single area system.

Unit commitment, static security analysis, state estimation, optimal power flow, automatic generation control and dynamic security analysis. High voltage AC: Cascaded transformers and Tesla coils. Impulse voltage: Shapes, mathematical analysis, codes and standards, single and multi-stage impulse generators, tripping and control of impulse generators. Breakdown in gas, liquid and solid dielectric materials. High voltage measurements and testing. Over-voltage phenomenon and insulation coordination. Lightning and switching surges, basic insulation level, surge diverters and arresters.

Computer Group. Review of 80x86 family of microprocessors. Instructions and data access methods in a 32 bit microprocessor; Representation of operands and operators; Instruction formats; Designing Arithmetic Logic Unit; Processor design: single bus, multi-bus architecture; Control Unit Design: hardwired, micro-programmed and pipe line; VLSI implementation of a microprocessor or part of a microprocessor design. Real Time design methodologies. Modeling for real time systems.

Reliable and Safe design for critical applications. Application examples: digital controls, robotics, on line systems, communication with real world signals and automatic control using feedback, feed-forward and adaptive control, control algorithm implementation. Courses offered by other Departments to EEE students. Computer Science and Engineering Department. Introduction to digital computers. Programming languages, algorithms and flow charts.

Structured Programming using C: Variables and constants, operators, expressions, control statements, functions, arrays, pointers, structure unions, user defined data types, input-output and files. In the first part, students will perform experiments to verify practically the theories and concepts learned in CSE In the second part, students will learn program design. In the second part, students will design systems using the principles learned in CSE Instructions and data access methods; Arithmetic Logic Unit ALU design: arithmetic and logical operations, floating point operations; Processor design: data paths- single cycle and multi cycle implementations; Control Unit design: hardware and micro-programmed Pipeline- pipelined data path and control, hazards and exceptions.

Memory organization: cache, virtual memory; Buses; Multiprocessors, type of multiprocessor performance, single bus multiprocessors, clusters. Types of media.

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Multimedia signal characteristic: sampling, digital representation, signal formats. Signal coding and compression: entropy coding, transform coding, vector quantization. Coding standards: H. Multimedia synchronization, security, QoS and resource management. Civil Engineering Department. CE Engineering Drawing 1. Introduction- lettering, numbering and heading; instrument and their use; sectional views and isometric views of solid geometrical figures.

Plan, elevation and section of multistoried building; building services drawings; detailed drawing of lattice towers. Mechanical Engineering. Introduction to sources of energy: Steam generating units with accessories and mountings; steam turbines. Introduction to internal combustion engines and their cycles, gas turbines. Refrigeration and air conditioning: applications; refrigerants, different refrigeration methods. Fluid machinery: impulse and reaction turbines; centrifugal pumps, fans, blowers and compressors. Basics of conduction and convection: critical thickness of insulation.

Sessional based on ME Industrial and Production Engineering. Management Functions and Organization: Evolution, management function: organization, theory and structure, span of control, authority delegation, manpower planning. Personal Management: Importance, need hierarchy, motivation, leadership, wage incentives, performance appraisal, participative management. Operation Management: Production planning and control PPC functions, quantitative methods applied in production, quality management, location and layout planning safety and loss management.

Cost and Financial Management: Elements of cost products, cost analysis, investment analysis, benefit cost analysis, risk analysis. Management Accounting: Cost planning and control, budget and budgetary control. Marketing Management: Concepts, strategy, sales promotion, patent laws. Technology Management: Management of innovation and changes, technology life cycle. Case studies. Physics Department. Waves and oscillations: Differential equation of simple harmonic oscillator, total energy and average energy, combination of simple harmonic oscillations, spring mass system, torsional pendulum; two body oscillation, reduced mass, damped oscillation, forced oscillation, resonance, progressive wave, power and intensity of wave, stationary wave, group and phase velocities.

Optics: Defects of images: spherical aberration, astigmatism, coma, distortion, curvature, chromatic aberration. Theories of light; Interference of light: Young's double slit experiment, displacement of fringes and its uses, Fresnel bi-prism, interference in thin films, Newton's rings, interferometers; Diffraction: Diffraction by single slit, diffraction from a circular aperture, resolving power of optical instruments, diffraction at double slit and N-slits, diffraction grating; polarization: Production and analysis of polarized light, Brewster's law, Malus law, polarization by double refraction, Nicol prism, optical activity, Polarimeters.

Thermal Physics: Heat and work- the first law of thermodynamics and its applications; Kinetic Theory of gases- Kinetic interpretation of temperature, specific heats of ideal gases, equipartition of energy, mean free path, Maxwell's distribution of molecular speeds, reversible and irreversible processes, Carnot's cycle, second law thermodynamics, Carnot's theorem, entropy, Thermodynamic functions, Maxwell relations, Clausius and Clapeyron equation. PHY Physics Sessional 1. Laboratory experiments based on PHY Electricity and Magnetism: Electric charge and Coulomb's law, Electric field, concept of electric flux and the Gauss's law- some applications of Gauss's law, Gauss's law in vector form, Electric potential, relation between electric field and electric potential, capacitance and dielectrics, gradient, Laplace's and Poisson's equations, Current, Current density, resistivity, the magnetic field, Ampere's law, Biot-Savart law and their applications, Laws of electromagnetic induction- Maxwell's equation.

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Modern Physics: Galilean relativity and Einstein's special theory of relativity; Lorentz transformation equations, Length contraction, Time dilation and mass-energy relation, photoelectric effect, Compton effect; De Broglie matter waves and its success in explaining Bohr's theory, Pauli's exclusion principle, Constituent of atomic nucleus, Nuclear binding energy, different types of radioactivity, radioactive decay law; Nuclear reactions, nuclear fission, nuclear fusion, atomic power plant. Mechanics: Linear momentum of a particle, linear momentum of a system of particles, conservation of linear momentum, some applications of the momentum principle; Angular momentum of a particle, angular momentum of a system of particles, Kepler's law of planetary motion, the law of universal Gravitation, the motion of planets and satellites, introductory quantum mechanics; Wave function; Uncertainty principle, postulates, Schrodinger time independent equation, expectation value, Probability, Particle in a zero potential, calculation of energy.

Laboratory experiments based on PHY Chemistry Department. Atomic Structure, quantum numbers, electronic configuration, periodic table. Properties and uses of noble gases. Different types of chemical bonds and their properties. Molecular structures of compounds. Selective organic reactions. Different types of solutions and their compositions. Phase rule, phase diagram of monocomponent system. Properties of dilute solutions.

Thermochemistry, chemical kinetics, chemical equilibria. Ionization of water and pH concept.

Electrical properties of solution. Volumetric analysis: acid-base titration, oxidation-reduction titrations, determination of Fe, Cu and Ca volumetrically. Mathematics Department. A large AC electric motor under load can be considered as a parallel combination of resistance and inductance:. Calculate the equivalent inductance L eq if the measured source current is Here is a case where scalar calculations R, G, X, B, Y are much easier than complex number calculations all Z would be.

Determine the total current and all component currents in this circuit, stating your answers the way a multimeter would register them:. I leave it to you to suggest where to insert the shunt resistor, what resistance value to select for the task, and how to connect the oscilloscope to the modified circuit. Calculate the total impedances complete with phase angles for each of the following inductor-resistor circuits:. Have your students explain how they solved for each impedance, step by step. You may find different approaches to solving the same problem s , and your students will benefit from seeing the diversity of solution techniques.

A doorbell ringer has a solenoid with an inductance of 63 mH connected in parallel with a lamp for visual indication having a resistance of ohms:. Calculate the phase shift of the total current in units of degrees in relation to the total supply voltage, when the doorbell switch is actuated. Suppose the lamp turned on whenever the pushbutton switch was actuated, but the doorbell refused to ring. Identify what you think to be the most likely fault which could account for this problem. The measured phase shift between voltage and current for this motor is 34 o , with voltage leading current.

Determine the equivalent parallel combination of resistance R and inductance L that is electrically equivalent to this operating motor. Challenge question: in the parallel LR circuit, the resistor will dissipate a lot of energy in the form of heat. Does this mean that the electric motor, which is electrically equivalent to the LR network, will dissipate the same amount of heat? Explain why or why not. If students get stuck on the challenge question, remind them that an electric motor does mechanical work , which requires energy.

Doorbell circuits connect a small lamp in parallel with the doorbell pushbutton so that there is light at the button when it is not being pressed. Suppose that such a doorbell circuit suddenly stops working one day, and the home owner assumes the power source has quit since the bell will not ring when the button is pressed and the lamp never lights. Although a dead power source is certainly possible, it is not the only possibility. Identify another possible failure in this circuit which would result in no doorbell action no sound and no light at the lamp.

After discussing alternative possibilities with your students, shift the discussion to one on how likely any of these failures are. How do either of these possibilities compare with the likelihood of the source failing as a result of a tripped circuit breaker or other power outage? Calculate the total impedance offered by these two inductors to a sinusoidal signal with a frequency of 60 Hz:. The purpose of this question is to get students to realize that any way they can calculate total impedance is correct, whether calculating total inductance and then calculating impedance from that, or by calculating the impedance of each inductor and then combining impedances to find a total impedance.

This should be reassuring, because it means students have a way to check their work when analyzing circuits such as this! Calculate the total impedance of this LR circuit, once using nothing but scalar numbers, and again using complex numbers:. Some electronics textbooks and courses tend to emphasize scalar impedance calculations, while others emphasize complex number calculations. While complex number calculations provide more informative results a phase shift given in every variable!

Calculate the total impedance offered by these two inductors to a sinusoidal signal with a frequency of Hz:. Determine the input frequency necessary to give the output voltage a phase shift of 75 o :. Discuss with your students what a good procedure might be for calculating the unknown values in this problem, and also how they might check their work. By having students outline their problem-solving strategies , everyone gets an opportunity to see multiple methods of solution, and you the instructor get to see how and if!

Determine the necessary resistor value to give the output voltage a phase shift of 44 o :. Determine the necessary resistor value to give the output voltage a phase shift of o :. Nothing special to note here, just practice with the impedance triangle and the capacitive reactance formula. Capacitors and inductors are complementary components - both conceptually and mathematically, they seem to be almost exact opposites of each other. Calculate the total impedance of this series-connected inductor and capacitor network:. Here, the complementary nature of inductive and capacitive reactances is plain to see: they subtract in series.

Challenge your students by asking them what the total impedance of this circuit would be if the two reactances were equal. Ask your students why one of the reactance terms under the radicand is positive and the other is negative. The way this equation is written, does it matter which term is negative? Challenge them to answer this question without using a calculator! Write an equation that solves for the admittance of this parallel circuit. Ask your students how they obtained the phase angle for this circuit. There is more than one way to calculate this! Now, suppose we take these same components and re-connect them in parallel rather than series.

Explain your answer. As usual, the real point of this question is to get students to think about the analytical procedure s they use, and to engage their minds in problem-solving behavior. Ask them why they think the circuits behave inductively or capacitively. What combination of components could you connect together in series to achieve this precise impedance? Students should be very familiar with how to calculate the impedance of a series-connected group of components, but calculating component values from an impedance figure may be a challenge to some.

Hint: if you are having difficulty figuring out where to start in answering this question, consider the fact that these two circuits, if equivalent in total impedance, will draw the exact same amount of current from a common AC source at 1 kHz. This is an interesting question, requiring the student to think creatively about how to convert one configuration of circuit into another, while maintaining the same total effect. As usual, the real purpose of a question like this is to develop problem-solving strategies, rather than to simply obtain an answer.

Calculate the total impedance of these parallel-connected components, expressing it in polar form magnitude and phase angle :. Some students may wonder why every side of the triangle is represented by a Y term, rather than Y for the hypotenuse, G for the adjacent, and B for the opposite. If students ask about this, remind them that conductance G and susceptance B are simple two different types of admittances Y , just as resistance R and reactance X are simply two different types of impedances Z.

Calculate the total impedance offered by these two capacitors to a sinusoidal signal with a frequency of 3 kHz:. This is not true, however. Impedances always add in series and diminish in parallel, at least from the perspective of complex numbers. This is one of the reasons I favor AC circuit calculations using complex numbers: because then students may conceptually treat impedance just like they treat DC resistance. The purpose of this question is to get students to realize that any way they can calculate total impedance is correct, whether calculating total capacitance and then calculating impedance from that, or by calculating the impedance of each capacitor and then combining impedances to find a total impedance.

A student measures voltage drops in an AC circuit using three voltmeters and arrives at the following measurements:. Upon viewing these measurements, the student becomes very perplexed. Why, then, is the total voltage in this circuit only Another student, trying to be helpful, suggests that the answer to this question might have something to do with RMS versus peak measurements. A third student disagrees, proposing instead that at least one of the meters is badly out of calibration and thus not reading correctly.

When you are asked for your thoughts on this problem, you realize that neither of the answers proposed thus far are correct. AC voltages still add in series, but phase must also be accounted for when doing so. Unfortunately, multimeters provide no indication of phase whatsoever, and thus do not provide us with all the information we need.

Challenge question: calculate a set of possible values for the capacitor and resistor that would generate these same voltage drops in a real circuit. Hint: you must also decide on a value of frequency for the power source. The first layer of this question regards the basic concepts of AC phase, while the second exercises troubleshooting and critical thinking skills. Be sure to discuss both of these topics in class with your students.

The answer to the challenge question is a matter of algebraic substitution. Calculate the total impedance offered by these three resistors to a sinusoidal signal with a frequency of 10 kHz:. State your answer in the form of a scalar number not complex , but calculate it using two different strategies:. This question is set up to be more complex than it has to be. Its purpose is to get students thinking in terms of parallel admittances, in a manner similar to parallel conductances. Calculate the total impedance offered by these three capacitors to a sinusoidal signal with a frequency of 4 kHz:.

This question is another example of how multiple means of calculation will give you the same answer if done correctly! Make note to your students that this indicates an answer-checking strategy! Calculate the total impedance of this RC circuit, once using nothing but scalar numbers, and again using complex numbers:.

Calculate the total impedance offered by these two capacitors to a sinusoidal signal with a frequency of Hz:. Due to the effects of a changing electric field on the dielectric of a capacitor, some energy is dissipated in capacitors subjected to AC. Generally, this is not very much, but it is there. This dissipative behavior is typically modeled as a series-connected resistance:. Calculate the magnitude and phase shift of the current through this capacitor, taking into consideration its equivalent series resistance ESR :. Compare this against the magnitude and phase shift of the current for an ideal 0.

Why or why not? Follow-up question 2: explain how the ESR of a capacitor can lead to physical heating of the component, especially under high-voltage, high-frequency conditions. What safety concerns might arise as a result of this? This is another reason why capacitors are generally favored over inductors in applications where either will suffice. Follow-up question: identify the consequences of a shorted capacitor in this circuit, with regard to circuit current and component voltage drops.

A technician needs to know the value of a capacitor, but does not have a capacitance meter nearby. In lieu of this, the technician sets up the following circuit to measure capacitance:. Explain how this system works, in your own words. Also, write the formula you would use to calculate the value of C x given f and R. The formula you would use looks like this:. Follow-up question: could you use a similar setup to measure the inductance of an unknown inductor L x? Explain why this might be a problem, and suggest a practical solution for it.

This method of measuring capacitance or inductance for that matter is fairly old, and works well if the unknown component has a high Q value. This is typically called leakage resistance , and it is modeled as a shunt resistance to an ideal capacitance:. Calculate the magnitude and phase shift of the current drawn by this real capacitor, if powered by a sinusoidal voltage source of 30 volts RMS at Hz:. Compare this against the magnitude and phase shift of the current for an ideal capacitor no leakage. Discuss with your students the fact that electrolytic capacitors typically have more leakage less R leakage than most other capacitor types, due to the thinness of the dielectric oxide layer.

Voltage divider circuits may be constructed from reactive components just as easily as they may be constructed from resistors. Take this capacitive voltage divider, for instance:. Calculate the magnitude and phase shift of V out. Also, describe what advantages a capacitive voltage divider might have over a resistive voltage divider.

Follow-up question 1: explain why the division ratio of a capacitive voltage divider remains constant with changes in signal frequency, even though we know that the reactance of the capacitors X C1 and X C2 will change. Follow-up question 2: one interesting feature of capacitive voltage dividers is that they harbor the possibility of electric shock after being disconnected from the voltage source, if the source voltage is high enough and if the disconnection happens at just the right time.