A 266-V battery, an inductor, and a resistor are connected in series as shown in

Question

A 266-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 four time constants?
1      V

    (b) At this time, what is the voltage across the inductor?
2      V     (a) What is the voltage across the resistor at the end of four time constants?
1      V

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

Explanation / Answer

Io =E/R =266/R

I =Ioe^(-t/T)

I =(266/R)e^(-t/T)

a)

given

t=5T

Vr =IR =[(266/R)e^(-t/T)]R

Vr =266 e^(-5T/T)

Vr =1.79 V

b)

dI/dt =-(266/R)(1/T)e^(-t/T)

since T=L/R

dI/dt =-(266/R)(R/L)e^(-t/T)

dI/dt=-(266/L)e^(-t/T)

VL =L(dI/dt)

VL=L*[(-266/L)e^(-t/T)]

VL =-266e^(-5T/T)

VL=-1.79 V

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