First slide

Writing potential drop across a open line

Question

In the circuit of fig. the final voltage drop across
the capacitor C is

NA

A

$\frac{{Vr}_{1}}{r_{1} + r_{2}}$
B

$\frac{{Vr}_{2}}{r_{1} + r_{2}}$
C

$\frac{V (r_{1} + r_{2})}{r_{2}}$
D

$\frac{V (r_{1} + r_{2})}{r_{1} + r_{2} + r_{3}}$

Solution

In steady state, the capacitor arm presents an infinite resistance. So the potential difference across C is that across.r₂,
Current through r₂ = V / (r₁+r₂)
P.D. across r₂=V r₂/ (r₁+r₂)

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