CP CALC Consider the circuit shown in Fig. P30.71. Switch
Chapter 30, Problem 79CP
(choose chapter or problem)
Consider the circuit shown in Fig. P30.79. Switch S is closed at time \(t=0\), causing a current \(i_{1}) through the inductive branch and a current \(i_{2}) through the capacitive branch. The initial charge on the capacitor is zero, and the charge at time 
is \(q_{2}) (a) Derive expressions for \(i_{1}), \(i_{2}) and \(q_{2}) as functions of time. Express your answers in terms of \(\varepsilon\),
\(R_{1}\), \(R_{2}\) and . For the remainder of the problem let the circuit elements have the following values: \(\varepsilon=48\) V, \(L=8.0\) H, \(C=20\) \(\mu \mathrm{F}\), \(R_{1}=25\) \(\Omega\), and \(R_{2}=5000\) \(\Omega\).(b) What is the initial current through the inductive branch? What is the initial current through the capacitive branch? (c) What are the currents through the inductive and capacitive branches a long time after the switch has been closed? How long is a “long time”? Explain. (d) At what time \(t_{1}) (accurate to two significant figures) will the currents \(i_{1}) and \(i_{2}) be equal? (Hint: You might consider using series expansions for the exponentials.) (e) For the conditions given in part (d), determine \(i_{1}). (f) The total current through the battery is \(i=i_{1}+i_{2}\). At what time \(t_{2}) (accurate to two significant figures) will i equal one-half of its final value? (Hint: The numerical work is greatly simplified if one makes suitable approximations. A sketch of \(i_{1}) and \(i_{2}) versus may help you decide what approximations are valid.)
Equation Transcription:
Text Transcription:
t=0
i_1
i_2
q_2
i_1
i_2
q_2
R_1
R_2
epsilon=48
L=8.0
C=20
muF
R_1=25
R_2=5000
t_1
i_1
i_2
i_1
i=i_1+i_2
t_2
i_1
i_2
