Homework 2
SJTU233
Problem 1
Find the impedance Zab in the circuit seen in the figure. Suppose that R = 5 Ω .
Part A
Express Zab in polar form.
Enter your answer using polar notation. Express argument in degrees.
ANSWER:
Zab =
= 32.0\cis{38.7}
Ω
Part B
Express Zab in rectangular form.
Express your answer in complex form using three significant figures.
ANSWER:
Zab =
Problem 2
Part A
= 25.0 + 20.0j
Ω
The circuit in has an impedance of 40+j20Ω at a frequency of 4500rad/s. Determine R and L.
Express your answers using three significant figures separated by a comma.
ANSWER:
R,L =
,
= 50.0, 22.2
Ω,mH
Part B
The circuit in has an impedance of 40−j20Ω at a frequency of 4500rad/s. Determine R and C.
Express your answers using three significant figures separated by a comma.
ANSWER:
Ω,μF
R,C =
,
= 50.0, 2.22
Problem 3
Part A
Find the steady-state expression for vo in the circuit of if ig=90cos10000tmA. Suppose
that vo(t)=V0cos(ωt+ϕ), where −180∘<ϕ≤180∘. Determine the values V0, ω, ϕ.
Express your answers using three significant figures separated by commas.
ANSWER:
V0,ω,ϕ =
,
Problem 4
Part A
,
4
= 6.36, 1.00×10 , 45.0
V,rad/s,∘
Use the node-voltage method to find Vo in the circuit in the figure when Vs= 150 ∠0∘V.
Enter your answer using polar notation. Express argument in degrees.
ANSWER:
Vo =
= 118\cis{-42.9}
V
Problem 5
Use the mesh-current method to find the steady-state expression for vo(t) in the circuit in if
va=18sin(4000t)V,
vb=12cos(4000t)V.
Write the steady-state expression for vo(t) as vo=Vocos(ωt+ϕ), where −180∘<ϕ≤180∘. Suppose that R =
750 Ω .
Part A
Find the numerical value of Vo.
Express your answer to three significant figures and include the appropriate units.
ANSWER:
Vo =
= 8.01
Part B
Find the numerical value of ϕ.
Express your answer using three significant figures.
ANSWER:
ϕ=
= 79.9
∘
Problem 6
The parameters in the circuit shown in the figure are R1=0.1Ω, ωL1=0.8Ω, R2=24Ω, ωL2=32Ω,
and VL= 320 +j0V.
Part A
Calculate the phasor voltage Vs.
Enter your answer using polar notation. Express argument in degrees.
ANSWER:
Vs =
= 329\cis{1.68}
V
Part B
Connect a capacitor in parallel with the inductor, hold VL constant, and adjust the capacitor until the
magnitude of I is a minimum. What is the capacitive reactance?
Express your answer in complex form.
ANSWER:
Z = -32.0
Part C
Connect a capacitor in parallel with the inductor, hold VL constant, and adjust the capacitor until the
magnitude of I is a minimum. What is the value of Vs?
Enter your answer using polar notation. Express argument in degrees.
ANSWER:
Vs =
= 322\cis{1.90}
V
Part D
Find the value of the capacitive reactance that keeps the magnitude of I as small as possible and that at
the same time makes
|Vs|=|VL|= 320 V.
Express your answer with the appropriate units.
ANSWER:
Z = -26.9
Problem 7
A load consisting of a 480 Ω resistor in parallel with a (5/9)μF capacitor is connected across the
terminals of a sinusoidal voltage source vg, where vg=160 cos5000tV.
Part A
What is the peak value of the instantaneous power delivered by the source?
Express your answer with the appropriate units.
ANSWER:
p=
= 71.1
Part B
What is the peak value of the instantaneous power absorbed by the source?
Express your answer with the appropriate units.
ANSWER:
p=
= -17.8
Also accepted:
= 17.8
Part C
What is the average power delivered to the load?
Express your answer with the appropriate units.
ANSWER:
P=
= 26.7
Part D
What is the reactive power delivered to the load?
Express your answer with the appropriate units.
ANSWER:
Q=
= -35.6
Part E
Does the load absorb or generate magnetizing vars?
ANSWER:
generates
Part F
What is the power factor of the load?
ANSWER:
power factor = 0.600
Part G
What is the reactive factor of the load?
ANSWER:
reactive factor = -0.800
Problem 8
Part A
A personal computer with a monitor and keyboard requires 60 W at 115 V (rms). Calculate the rms value
of the current carried by its power cord.
Express your answer with the appropriate units.
ANSWER:
Ieff =
= 0.522
Part B
A laser printer for the personal computer is rated at 90 W at 115 V (rms). If this printer is plugged into the
same wall outlet as the computer, what is the rms value of the current drawn from the outlet?
Express your answer with the appropriate units.
ANSWER:
Ieff =
= 1.30
Problem 9
The periodic current shown in the figure dissipates an average power of 1050 W in a resistor. (This is a
fun question, think clearly!)
Part A
What is the value of the resistor?
Express your answer with the appropriate units.
ANSWER:
R=
= 7.88
Problem 10
The two loads shown in can be described as follows: Load 1 absorbs an average power of 10 kW and
delivers 4 kVAR of reactive power; load 2 has an impedance of (60+j80) Ω. The voltage at the terminals
of the loads is 15002√cos100πtV.
Part A
Find the rms value of the source voltage.
Express your answer to four significant figures and include the appropriate units.
ANSWER:
Vgrms =
= 1508
Part B
Determine by how many time is the load voltage out of phase with the source voltage by finding the value
of (θVL−θVg)/ω, where θVL and θVg are the phase angles of the voltages VL and Vg respectively,
and ω is the angular frequency of the voltages.
Express your answer to three significant figures and include the appropriate units.
ANSWER:
t=
= 8.20
Part C
Does the load voltage lead or lag the source voltage?
ANSWER:
leads
Problem 11
A factory has an electrical load of 1600 kW at a lagging power factor of 0.8. An additional variable power
factor load is to be added to the factory. The new load will add 360 kW to the real power load of the
factory. The power factor of the added load is to be adjusted so that the overall power factor of the factory
is 0.97 lagging.
Part A
Specify the reactive power associated with the added load.
Express your answer with the appropriate units.
ANSWER:
Q=
= -709
Part B
Does the added load absorb or deliver magnetizing vars?
ANSWER:
delivers
Part C
What is the power factor of the additional load?
ANSWER:
pf = = 0.453
Part D
Assume that the voltage at the input to the factory is 2100 V (rms). What is the rms magnitude of the
current into the factory before the variable power factor load is added?
Express your answer with the appropriate units.
ANSWER:
|IL| =
= 952
Part E
What is the rms magnitude of the current into the factory after the variable power factor load has been
added?
Express your answer with the appropriate units.
ANSWER:
|IL| =
= 962
Problem 12
The variable resistor R in the circuit shown in is adjusted until the average power it absorbs is maximum.
Suppose that Vs=350∠0∘V (rms).
Part A
Find the value of the resistor R required for the maximum average power absorbed by it.
Express your answer to three significant figures and include the appropriate units.
ANSWER:
R = 400
Part B
Find the maximum average power for the resistor R.
Express your answer to three significant figures and include the appropriate units.
ANSWER:
P=
= 7.66
Part C
Find a resistor from the table shown in that would have the most average power delivered to it.
Express your answer to three significant figures and include the appropriate units.
ANSWER:
R = 390