Download PHYS 222 Worksheet 22 RL and LC Circuits

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PHYS 222
Worksheet 22 – RL and LC Circuits
Supplemental Instruction
Iowa State University
Alek Jerauld
PHYS 222
Dr. Paula Herrera-Siklódy
3/19/12
Useful Equations
L
R
i(t ) 
RL Circuits: time constant
 1 et 




R
i(t )  I0e

t

Current in RL circuits (growth)
Current in RL Circuits (decay)
 1
LC
LC Circuit Angular Frequency
1
U  LI 2
2
Energy stored in an inductor
Related Problems
1) A 15.0 ohm resistor and a coil are connected in series with a 6.30-V battery with
negligible internal resistance and a closed switch. (Book 30.20)
(a) At 2.00 ms after the switch is opened the current has decayed to 0.210 A. Calculate the
inductance of the coil.
I0 

 0.42 A
R

t
L/ R
tR
 0.0433 H
 i 
ln  
 I0 
(b) Calculate the time constant of the circuit.
L
   2.89 ms
R
i(t )  I 0e
L
(c) How long after the switch is opened will the current reach 1.00% of its original value?
i(t )  I0e
 0.01I 0
t

t
 I0e   t   ln  0.01  13.3 ms
2) A 7.60-nF capacitor is charged up to 13.0 V, then disconnected from the power supply
and connected in series through a coil. The period of oscillation of the circuit is then
measured to be 8.60×10−5 s. (Book 30.29)
(a) Calculate the inductance of the coil.

1
LC
2
T
2
1
T2


 L  2  0.0247 H
T
4 C
LC

(b) Calculate the maximum charge on the capacitor.
Max charge occurs when voltage across capacitor is max, with means all the energy is
stored in the capacitor:
Q  CV  9.88(108 ) C
(c) Calculate the total energy of the circuit.
CV 2
U
 6.42(107 ) J
2
(d) Calculate the maximum current in the circuit.
LI 2 max CV 2
CV 2
U max 

 I max 
 7.22(103 ) A
2
2
L
3) An LC circuit containing an 86.0-mH inductor and a 1.50-nF capacitor oscillates with a
maximum current of 0.760 A. (Book 30.33)
(a) Calculate the maximum charge on the capacitor.
LI 2 max Q 2
U max 

 Qmax  I max LC  8.63(106 ) C
2
2C
(b) Calculate the oscillation frequency of the circuit.

1
f 

 1.4(104 ) Hz
2 2 LC
(c) Assuming the capacitor had its maximum charge at time t= 0, calculate the energy
stored in the inductor after 2.45 ms of oscillation.
LI 2
U max 
2
 t 
I  I max sin(t )  I max sin 

 LC 
2
 U max
LI 2
 t 
 max sin 
  0.0189 J
2
 LC 