23.55 Part A Find the characteristic time for this circuit. ? the answer should

Question

23.55

Part A

Find the characteristic time for this circuit. ?

the answer should be in  ms

Part B

What is the current supplied by this battery two characteristic time intervals after closing the switch?

the answer should be in  mA

Part C

What is the current supplied by this battery a long time after the switch is closed?

the answer should be in mA

Problem 23.55 Part A The circuit shown in the figure (Figure 1) consists of a 6.4- V battery, a 29-mH inductor, and four 52-52 resistors. Find the characteristic time for this circuit. Express your answer using two significant figures. Figure 1 of 1 T= 86.7 ms Submit My Answers Give Up Incorrect; Try Again; 5 attempts remaining Part B What is the current supplied by this battery two characteristic time intervals after closing the switch? Express your answer using two significant figures.

Explanation / Answer

Here,

R = 52 Ohm

L = 29 mH = 0.029 H

part A)

RL = 2R * R/(R + 2R) + R

Rl = 5R/3

RL = 5 * 52/3 Ohm

RL = 86.7 Ohm

characteristic time = L/RL

characteristic time = 0.029/86.7

characteristic time = 0.335 *10^-3 H

characteristic time = 0.335 mH

b)

after two time intervals

I = Io * (1 - e^(-t/T))

I = 6.4/(86.7) * (1 - e^(-2))

I = 0.0638 A = 63.8 mA

the current supplied is 63.8 mA

c)

after a long time

as the inductor will be short circuited

Io = V/RL

Io = 6.4/(86.7)

Io = 0.0738 A

the current supplied by this battery a long time after the switch is closed is 73.8 mA

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