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The arrangement shown which is confined in a vertical plane has two rails inclined at angle $θ$ with horizontal. A horizontal rod of length $l$ moves on the rails with constant speed $v,$ in the region with transverse field $B$ . Choose the correct alternatives. The rod starts moving at time $t = 0$

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At $t = 0,$ current in the circuit is $\frac{2 B V l \sin θ}{r}$

At $t = \infty,$ current in the circuit is $\frac{B l v \sin θ}{r}$

At any time $t ($ except at $t = 0)$ point $A$ is at higher potential than point $B$

At any time $t ($ except at $t = 0)$ point $D$ is at lower potential than $C$

answer is A, B.

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Detailed Solution

At t=0, no current flows through the inductor and at t = $\infty$ , no current flows through through the capacitor.

The induced emf across the rod,

$e = B v l \sin θ$

The equivalent resistance between $B$ and $D$ is $= \frac{r}{2}$

Current $, i = \frac{e}{\frac{r}{2}} = \frac{2 B v l \sin θ}{r}$

Also, $V_{A} > V_{B}$

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