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Electrostatic Potential And Capacitance

Question

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A capacitor is charged and then made to discharge through a resistance. The time constant is t. In what time will the potential difference across the capacitor decrease by 10 %?

τ ln 0.1

τ ln 0.9

τ ln $\frac{10}{9}$

τ ln $\frac{11}{10}$

Solution

C.

τ ln $\frac{10}{9}$

As, we know that

q = q₀ e^-t/λ

According to the question

V_C = $\frac{q}{C}$

= $\frac{q_{0}}{C}$ e^-t/λ

$\frac{q_{0}}{10} = \frac{q_{0}}{C}$ e^-t/λ

e^t/λ = $\frac{10}{9}$

⇒ t = τ ln $\frac{10}{9}$

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