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# Circuit analysis problem

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Question 1. (16 Points, 2 pts each)

a. Which is better for transmission of electric power over long distances: DC low voltage or AC high?
b. Where in the Washington DC area is there a statue of Joseph Henry
c. What is the SI (MKS) unit of inductance?
d. Write an equation for the terminal relationship for an inductor?
e. Write an equation for the energy stored in an inductor
f. An inductor has a terminal voltage v(t) = V0Cos (t). What is the voltage phasor?
g. A passive circuit element has the following voltage and current signals across its terminals: v(t) = 2000cos(30t) and i(t)= 10sin(30t). Is the element a capacitor, inductor or resistor?
h. Write the phase difference between the voltage and current across a load with impedance Z = 2+2j Ohms under AC steady state conditions?

Question 2. (9 Points)

In answering the following questions please refer to the curves a-I above.

a. Voltage across a capacitor has the time dependence which looks like curve d.
Which curve could represent the time dependence of current through the capacitor?

b. Current through a resistor has the time dependence which looks like curve g.
Which curve could represent the time dependence of voltage across the resistor?

c. Voltage across an inductor has the time dependence, which looks like curve i.
Which curve could represent the time dependence of current through the inductor?

Question 3. (15 Points)
On the schematic shown below, two voltages and two currents are given.
Find all of the other voltages and write them in the rectangles next to the resistors.

Question 4 (20 pts)
For t > 0 the voltage across a 1 F capacitor is given by the expression

where t is the time in seconds.
a) Calculate the current flow in the capacitor, and sketch a graph of your answer
b) Calculate the instantaneous power flow in the capacitor, and sketch a graph of your answer
c) At what time is the instantaneous power flow maximum
d) What is the energy stored in the capacitor for t = 2 seconds.

Question 5 (20 pts)

Consider the circuit shown on the left with vs1 (t) = 50 sin (t) and vs2(t) = 30 sin (t) and frequency 1 kHz.

a) Write the KCL and KVL equations for the circuit in phasor form. (Cleary label your diagram)
b) Calculate the current phasor for is1(t).
c) Calculate is1(t)

Question 6 (20pts)

A load that consists of an inductor, resistor, and a capacitor is connected across a voltage source between points A and B, as shown on schematic below. The voltage source produces sinusoidal signal with amplitude of 10 Volts at a frequency of 200 Hz.

a. current,
b. power factor
c. average power dissipation.

##### Solution Summary

The problem has been solved step by step using Kirchhoff's current and voltage laws.

##### Solution Preview

Question 5 (20 pts)

I1 I2

Consider the circuit shown on the left with vs1 (t) = 50 sin (t) and vs2(t) = 30 sin (t) and frequency 1 kHz.

a) Write the KCL and KVL equations for the circuit in phasor form. (Cleary label your diagram)
b) Calculate the current phasor for is1(t).
c) Calculate is1(t)

Solution :

Inductive reactance (magnitude) = ωL = 2ΠfL = 2Π x ...

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