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Find the current in the sliding cod AB (resistance = R) for the arrangement shown in figure. B is constant and is out of the paper. Parallel wires have no resistance, v is constant. Switch S is closed at time t = 0.

Answers (1)

By applying KVL in the given circuit, we have

-L\frac{dI}{dt}+vBd=IR\; or\; L\frac{dI}{dt}+IR=vBd

This is the linear differential equation. On solving,

I=\frac{vBd}{R}+Ae^{-\frac{Rt}{ L}}

At \; t=0, I=0

\Rightarrow A=-\frac{vBd}{R}\Rightarrow I=\frac{vBd}{R}\left ( 1-e^{\frac{-Rt}{L}} \right )

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