# 1. A 1.2 µF capacitor is initially charged to 50V. How much energy is

```1. A 1.2 &micro;F capacitor is initially charged to 50V.
How much energy is stored in the capacitor?
What will be the voltage on the capacitor after it has been discharged by a 10 &micro;A
current for two seconds?
2. Consider the circuit below. After the switch has been closed for a long time,
determine the value of the currents as referenced in the schematic.
R3 = R4 = R5 = 10kΩ, L1 = 1mH, C1 = 100&micro;F.
TCLOSE = 0
1
2
R3
i2
i1
R4
is
2
L1
C1
R5
Vs= 10V
1
is = _________
i1 = __________
i2 = __________
2
3. The switch in the circuit below has been closed for a long time. At t=0 the switch
opens. I3 = 5mA, R4 = 10kΩ and C3 = 1.2&micro;F. If the voltage on the capacitor at t=0
is 25V, develop an expression for the voltage across the capacitor V(t) for t&gt;0. Show
5mA
Switch open @ t=0
1
I3
R4
10k
V(t)
+
-
V(t) = ____________________________
C3
1.2uF
4. For the circuit shown below, I(t) = 100 cos(103t + 15), R = 10Ω, L1 = 5mH, L2,
L3 = 10mH and C = 100&micro;F
1
L1
2
2
I1
L2
R1
I(t)
2
1
L3
C1
1
What is the RMS value of I(t)?
IRMS = _______________
What is the phasor representation of the current source?
Is = __________________
What is the phasor current through R1 ?
IR1= ___________________
What is the phasor voltage across the capacitor Vc
Vc = __________________
5. Consider the circuit shown below. I(t) = 40 cos(100t) A
C2
V1
V2
500 uF
2
I2
I(t)
R2
40
R3
10
L4
0.2 H
1
Write a simplified node equation for the V1 node.
(_________________) V1 + (________________) V2 = ___________
Write a simplified node equation for the V2 node.
(___________) V1 + (_________) V2 = ___________
Solve for the phasor voltages(magnitude and phase) V1 = ____________
V2 = ____________
6. For the circuit below, load A consumes 5kW at a 80% leading power factor. Load
B consumes 10 kW at 90% lagging power factor. The voltage source provides
5kVRMS.
5KV (rms)
A
B
Draw the power triangle for Load A. Label the power angle and all sides with
magnitude and sign.
Draw the power triangle for Load B. Label the power angle and all sides with
magnitude and sign.
Draw the power triangle for the Source. Label the power angle and all sides with
Source
magnitude and sign.
7. The input signal Vin(t) =
1 1
1
1
+ cos(1000πt ) +
cos(3000πt ) +
cos(5000πt )
2 π
3π
5π
is applied to the input of a system with a transfer function shown graphically below.
H(f)
Vin(t)
Vout(t)
|H(f)|
/_H(f)
2
0
-45
-90
1000
2000
3000
f (Hz)
1000
2000
3000
f (Hz)
Looking at the magnitude graph of H (f), what kind of ideal filter is represented?
|H(f)| represents an ideal _____________ filter.
Write a time domain expression for Vout(t)
Vout(t) = ____________________________________
8. Given the cascaded system shown below, assume that the loading effects of the
second filter have been accounted for and that all phasors have a common frequency.
H1(f)
Vin
H2(f)
Vout
If Vin = 15/_ 0 , H1(f) = 3/_-25 , and H2(f) = 10/_ +15, write an expression for the phasor
output of the cascaded system Vout
.
Vout = ____________________
Using the values of H1(f) = 3/_-25 , and H2(f) = 10/_ +15, what is the magnitude of
H1(f) and H2(f) in decibels?
| H1(f)|dB = __________dB
9. In the circuit below, R =
| H2(f)|dB = ___________dB
500
Ω and C= 2&micro;F.
2π
What is the transfer function? ________________________
At what frequency, in Hertz, will the amplitude of the output signal, Vout(t) =
fb = ___________Hz
R
Vin(cos wt)
Determine the phase angle for Vout at f = fb?
C
Vout
_________________
Vin
2
```