Solutions to Homework Questions 7

Physics 112 Homework 7 (solutions) (2004 Fall)
Chapt21, Problem-33: An RLC circuit is used to tune a radio to an FM station broadcasting at 88.9 MHz.
The resistance in the circuit is 12.0 ! and the capacitance is 1.40 pF. What inductance should be present in the circuit
Solution:
The resonance frequency of the circuit should match the broadcast frequency of the station.
1
f 0 =
2! LC gives L = 1
4! 2 f 2 0
C ,
1
or L =
2 .29 µH
4! 2 88.9 "10 6 Hz
( ) 2 ( 1.40 " 10 #12 F) = 2 .29" 10#6 H =
Chapt21, Problem-35: The AM band extends from approximately 500 kHz to 1 600 kHz. If a
2.0-µH inductor is used in a tuning circuit for a radio, what are the extremes that a capacitor must reach in
order to cover the complete band of frequencies
Solution:
1
f 0 =
2! LC , so C = 1
4! 2 f 2 0
L
For f 0 = f 0
For f 0 = f 0
( ) min
= 500 kHz = 5.00 !10 5 Hz ,
C = C max =
1
( ) 2 ( 2.0 " 10 #6 H) = 5.1" 10#8 F =
4! 2 5.00 "10 5 Hz
( ) max
= 1600 kHz = 1.60! 10 6 Hz ,
C = C min =
1
( ) 2 ( 2.0 " 10 #6 H) = 4.9 " 10#9 F =
4! 2 1.60 " 10 6 Hz
51 nF
4.9 nF
Chapt21, Problem-41: A transformer on a pole near a factory steps the voltage down from 3600 V to 120V.
The transformer is to deliver 1 000 kW to the factory at 90% efficiency. Find (a) the power delivered to the primary, (b) the
current in the primary, and (c) the current in the secondary.
Solution:
(a) At 90% efficiency, (! av ) output
= 0.90 (! av ) input
.
Thus, if (! av ) output
= 1000 kW ,
(
the input power to the primary is (! av ) input
= ! av ) output 1000 kW
= =
0.90 0.90
1.1! 103 kW
(
(b) I 1, rms = ! av ) input
= 1.1 #103 kW
= 1.1# 106 W
"V 1, rms
"V 1, rms
3600 V = 3.1! 102 A
(
(c) I 2, rms = ! av ) output 1000 kW
= = 1.0 #106 W
"V 2, rms
"V 1, rms
120 V = 8.3 !103 A
3