Electric Circuits I (EELE 2310)

Electric Power Engineering site.iugaza.edu.ps/ajasser Assad Abu-Jasser, PhD Electric Power Engineering site.iugaza.edu.ps/ajasser ajasser@iugaza.edu.ps

Inductance, Capacitance and Mutual Inductance Chapter Six Inductance, Capacitance and Mutual Inductance

The Inductor ʋ≡ voltage in Volts (V) L≡ inductance in Henry (H) i ≡ current in Amperes (A)

Example 6-1 Determine the Voltage, Given the Current The independent current source in the circuit shown generates zero current for t˂0 and a pulse 10te-5t A, for t˃0. Sketch the current waveform. At what instant of time the current is maximum? Express the voltage across the terminals of the 100 mH inductor as a function of time. Sketch the voltage waveform. Are the voltage and the current at a maximum at the same time? At what instant of time does the voltage change polarity? Is there ever an instantaneous change in the voltage across the inductor? If so, at what time? i=0 t˂0 i=10te-5t t˃0 e) no f) at 0.2 s g) yes, at t=0

Current in an Inductor In terms of the Voltage Across the Inductor

Example 6-2 Determine the Current, Given the Voltage ʋ=20te-10t t˃0 The voltage pulse applied to the 100 mH inductor is 0 for t˂0 and given by the expression ʋ(t)=20te-10t V, for t˃0. Also assume ʋ=0 for t ≤ 0. Sketch the voltage as a function of time. Find the inductor current as a function of time. Sketch the current as a function of time.

Power and Energy in The Inductor

Example 6-3 Determine the Current, Voltage, Power, and Energy The independent current source in the circuit shown generates zero current for t˂0 and a pulse 10te-5t A, for t˃0. Plot i, ʋ, p, and ω versus time. In what time interval is energy being stored in the inductor? In what time interval is energy being extracted from the inductor? What is the maximum energy stored in the inductor? Evaluate the integral Repeat (a)-(c) for a voltage pulse of ʋ(t)=20te-10t V, for t˃0 and ʋ=0 for t ≤ 0. In (f), why is there a sustained current in the inductor as the voltage approaches zero? ʋ=0 t≤0 ʋ=20te-10t t˃0 i=0 t≤0 i=10te-5t t˃0

The Capacitor ʋ≡ voltage in Volts (V) C≡ capacitance in farad (F) i ≡ current in Amperes (A)

Example 6-4 Determine the Current, Power, and Energy The voltage pulse described by the following equation is impressed across the terminals of a 0.5 µF capacitor: Derive expression for the capacitor current, power, and energy. Sketch the voltage, current, power, and energy as functions of time. Line up the plots vertically. Specify the interval of time when energy is being stored in the capacitor. Specify the interval of time when energy is being delivered by the capacitor. Evaluate the integrals

Example 6-5 Determine the Voltage, Power, and Energy An uncharged 0.2 µF capacitor id driven by a triangular current pulse. The current pulse is described by: Derive the expressions for the capacitor voltage, power, and energy for each of the four time intervals needed to describe the current. Plot i, Ʋ, p, and ω versus t. Align the plots vertically. Why does the voltage remain on the capacitor after the current returns to zero?

Summary

Series-Parallel Combination Inductances in Series

Series-Parallel Combination Inductance in Parallel

Series-Parallel Combination Capacitance in Series

Series-Parallel Combination Capacitance in Parallel

Mutual Inductance

Dot Convention of Mutually Coupled Coils When the reference direction for a current enters the dotted terminal of a coil, the reference polarity of the voltage that it induces in the other coil is positive at its dotted terminal When the reference direction for a current leaves the dotted terminal of a coil, the reference polarity of the voltage that it induces in the other coil is negative at its dotted terminal

Procedure for Determining Dot Markings

Example 6.6 Mesh-current for Magnetically Coupled Circuits Write a set of mesh-current equation that describe the circuit in terms of the currents i1 and i2. Verify that if there is no energy stored in the circuit at t=0 and if ig=16-16e-5t A, the solutions for i1 and i2 are:

Review of Self-Inductance

The Concept of Mutual Inductance

Mutual Inductance In Terms of Self-Inductance

End of Chapter Six