Power Systems
Homework #1
Problem #1 (25 pts). For a sinusoidal voltage V(t)=100*cos(314*t), find the RMS
voltage, periodic time, frequency, and the instantaneous value of the voltage at
t=5ms.
Answer:
Vrms=100/sqrt(2)=70.7 V
Periodic time: T=2*pi/314=0.02 s
Frequency: f=314/2/pi=50 Hz
V(t=5ms)=100*cos(0.5pi)=0
Vmax (V) Vrms (V) Omega (1/s) T (s)
f (Hz)
t (s)
v(t) V
100 70.71068
314 0.02001 49.97465
0.005 0.079633
Problem #2 (25 pts). Find the Norton equivalent circuit of the circuit shown below.
Answer: (if the student use Rth=1 Ohm, it will also be correct)
Ino=Vth/Rth=4 A, Rno=Rth =2.5 Ohm
Problem #3 (50 pts). Use mesh analysis, solve the currents flowing through the
resistors in the following circuit:
Answer:
KVL
Mesh 1 (left, clock-wise current): V1 + R1*I1 +R2*(I1-I2)=0
Mesh 2 (right, clock-wise current): -V2 + R2*(I2-I1)+R3*I2=0
i.e.,
Mesh 1: 28 - 4*I1 -2*(I1-I2)=0
Mesh 2: -7 - 2*(I2-I1) - 1*I2=0
Mesh 1: 6*I1 - 2*I2=28
Mesh 2: -2*I1+3*I2 =-7
Solve for I1 and I2 =>
I1=5A
I2=1A
The current flowing through R1 is I1 (left-to-right), 5A
The current flowing through R2 is I1-I2 (top-to-bottom), 4A
The current flowing through R3 is I2 (left-to-right), 1A