EE 1050 Homework #19
Due: Tue 11/13/01
A.Stolp
10/31/01
Read section 6.2, p 288 in your textbook.
Note: In the following problems, you may assume voltages and currents are RMS and transformers are ideal unless
stated otherwise.
rad
1. Compute the power factor for an inductive load withL 100. mH and R 0.4 . Ω assume ω 377.
s
Note: L and R are in series and together constitute the load.
2. Problem 6.21 in textbook, p.324.
f hint: Ave energy =
Q
2. ω
3. Problem 6.23 in textbook.
4. a) Problem 6.27 in textbook.
b) Find the value of the capacitor assuming f = 60Hz,
5. Consider the circuit at right. The resistor and capacitor together make up the load.
Load
a) Find the load impedance of the circuit.
4. Ω
R
vs
155.6. V . cos( 377. t )
b) Compute the average power dissipated by the load.
RS
6. a) Compute the average power dissipated by the load (R L
and C L taken together).
b) Compute the power dissipated by the internal
source resistance (RS) in this circuit.
1000 . µF
C
Load
110. V
rms
VS
ω
2. Ω
377.
Read section 6.3, p 301 in your textbook.
Assume the following transformers are ideal unless stated otherwise.
CL
100. µF
rad
s
RL
16. Ω
7. An ideal transformer has 240 turns on the primary winding and 20 turns on the secondary. If the primary is
connected across a 110-V (rms) generator, what is the rms output voltage?
8. A transformer has n 1 = 350 turns and n2 = 2000 turns. If the input voltage is v(t) = (170 V)cos(ωt), what rms
voltage is developed across the secondary coil?
9. A step-up transformer is designed to have an output voltage of 2200-V (rms) when the primary is connected
across a 110-V (rms) source.
a) If there are 80 turns on the primary winding, how many
turns are required on the secondary?
b) If a load resistor across the secondary draws a current of 1.5 A,
what is the current in the primary, assuming ideal conditions?
10. The primary current of an ideal transformer is 8.5 A when the primary voltage is 77 V. Calculate the voltage
across the secondary when a current of 1.4 A is delivered to a load resistor.
EE 1050 Homework #19
11. An ideal transformer has a turns ratio (N = N2/N1) of 0.6667. It is desired to operate a 200Ω resistive load at
150-V (rms).
a) Find the secondary and primary currents.
b) Find the source voltage (V 1).
c) Find the power dissipated in the load resistor and the power delivered to the primary from the source.
d) Find the impedance the source sees looking into the primary winding by calculating Zeq = ZL / N2 and again by
calculating V1 / I1.
12. For the ideal transformer shown in the figure, find v o(t) if vs(t) is 294Vcos(377t).
13. A transformer is rated at 13,800/480 V, 100 kVA, 60 Hz.
(Note: kVA stands for kilo-Volt-Amp, it is the
transformer's voltage rating times its current rating.) Find
the allowable primary and secondary currents at a supply
voltage of 13,800 V at 100% power factor. Repeat for a
power factor of 50%.
15.
14. An ideal transformer has a rating of 500/125 V, 10 kVA,
60 Hz. It is loaded with an impedance of 10Ω at 75% pf
(0.75). The source voltage applied to the primary
winding is 480 V (rms). Find
a) the load voltage
b) the load current
c) the kVA delivered to load
d) the power delivered to load
e) the primary current
f) the power factor of primary
g) the impedance the source sees looking into primary.
Answers
1. pf
P
2. g answer is at right:
0.0106
θ
3., 4., & 5. See textbook
5. a) Z
4.8 . Ω. e
j. 33.5. deg
Q
3
b) P av 2.102. 10 . W
b) 101.46 . W
S
d) 450Ω
14. a) 120 V
e) 3 A
b) 12 A
c) 1.44 kVA
d) 1.08 kW
b) 400. kW c) 320. kW d) 280. kW e) 0.75
EE 1050 Homework #19
41.2. deg
420. VAR
6. a) P av 595. W
7. 9.17 V
8. 687 V
9. a) 1600 turns
b) 30 A
10. 467.5 V
11. a) 0.75 A, 0.50 A
b) 225 Vc) 112.5 W
12. 71.7Vcos(377t)
13. 7.25 A, 208 A, any pf
15. a) 870. A
480. W
f) 0.75
g) 160 Ω
638. VA