Consider the figure shown below. The switch is initially set at position b. Ther

Question

Consider the figure shown below. The switch is initially set at position b. There is no charge nor current around the upper loop while at position b. At t1 = 0 the switch is set to position a.

With the switch still in position a, what is the power consumption through the resister R at time t1 = 1/2tauL, where tauL is the time constent of the LR loop? Pca = epsilon2/R (1 + e-1/2)2 Pca = epsilon2/R (1 + e+1/2)2 Pca = epsilon2/R Pca = epsilon2/R (1 - e-1/2)2 Pca = epsilon2/R (e-1/2)2 Pca = epsilon2/R (e+1/2)2 Pca = epsilon2/R (1 - e+1/2)2

Explanation / Answer

Option 4 is the correct answer.

Here is the explanation.

let T is time constant of the ckt.
Current through resistor, at time t

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

= (e/R)*(1 - e^(-t/T) )

at t = T/2

I = (e/R)*(1 - e^(-1/2) )

power consumption through R = I^2*R

= [ (e/R)*(1 - e^(-1/2) ) ]^2*R

= (e^2/R)*(1 - e^(-1/2) )^2

so, Option 4 is the correct answer.

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