First slide

Writing potential drop across a open line

Question

In the circuit shown, switch S₂ is closed first and is kept closed for a long time. Now S₁ is closed. Just after that instant, the current through S₁ is

Moderate

A

$\frac{ε}{R_{1}} t o w a r d s r i g h t$
B

$\frac{ε}{R_{1}} t o w a r d s l e f t$
C

zero
D

$\frac{2 ε}{R_{1}}$

Solution

Just before S₁ is closed, the potential difference across capacitor 2 is $2 ε$ .
Just after S₁ is closed, the potential differences across capacitors 1 and 2 arc 0 and $2 ε$ respectively.
If we take potential of C and D to be zero, then $V_{A} = ε, V_{B} = 2 ε$
Since V_B > V_A, so current will flow $i = \frac{2 ε - ε}{R_{1}} = \frac{ε}{R_{1}} towards lef t$

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