A 192-V battery, an inductor, and a resistor are connected in series as shown in

Question

A 192-V battery, an inductor, and a resistor are connected in series as shown in the diagram below. A two-way switch makes it possible to include or exclude the battery. The switch that had been in position 1 for a long time is suddenly moved to position 2. (Enter your answers to at least two decimal places.)

(a) What is the voltage across the resistor at the end of five time constants?
V =?

(b) At this time, what is the voltage across the inductor?
V?

Then part 2.

At what two times in the first period following t = 0 does the instantaneous voltage in 87 Hz AC equal Vrms?

(Enter the first two times t1 and t2. Assume zero phase shift.)

Explanation / Answer

a) Voltage across the resistor at time t

V = Vmax*(1 - e^(-t/T))

at t = 5*T

V = Vmax*(1 - e^(-5*T/T))

= Vmax*(1 - 1/e^5)

= 192*(1 - 1/2.718^5)

= 190.71 volts

b) voltage across inductor at tis time, vL = Vmax - VR

= 192 - 190.71

= 1.29 volts

2) Vrms = Vmax/sqrt(2)

= 192/1.414

= 135.76 volts

we know, voltage of ac source,

v = Vmax*sin(wt)

Vrms = Vmax*sin(w*t)

Vmax/sqrt(2) = Vmax*sin(2*pi*t)

1/1.414 = sin(2*pi*87*t)

2*pi*f*t = sin^-1(1/1.414)

2*pi*f*t = 0.7854

t = 0.7854/(2*pi*87)

= 1.44*10^-3

= 1.44 ms

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