The circuit shown in the figure (Figure 1) consists of a 5.8- V battery, a 35-mH

Question

The circuit shown in the figure (Figure 1) consists of a 5.8- V battery, a 35-mH inductor, and four 55-ohm resistors. Find the characteristic time for this circuit. Express your answer using two significant figures. What is the current supplied by this battery two characteristic time intervals after closing the switch? Express your answer using two significant figures. What is the current supplied by this battery a long time after the switch is closed? Express your answer using two significant figures.

Explanation / Answer

a)

for the resistances

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

Req = 55 + 55 * (2 * 55)/(55 + 2 * 55)

Req = 91.7 Ohm

characteristic time = Req * L

characteristic time = 91.7 * 35 *10^-3 s

characteristic time = 3.21 s

part B)

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

I = (5.8/91.7) * (1 - e^(-2))

I = 0.0547 A = 54.7 mA

the current supplied by the battery is 54.7 mA

part C)

after a long time

I = Io

I = 5.8/91.7

I = 0.0632 A = 63.2 mA

the current in the battery after a long time will be 63.2 mA

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