A capacitor is initially uncharged in an RC circuit. Switch S1 is closed while S2 stays open, charging the capacitor through a resistor from a source of emf V. The circuit's time constant is τ. Which statement is correct?

Question

Accepted Answer

after a time 2τ, the charge on the capacitor equals CV(1 - e⁻²). For RC charging, q(t) = CV(1 - e^(-t/τ)). At t = 2τ: q = CV(1 - e⁻²) — correct. At t = τ: q = CV(1 - e⁻¹) ≈ 0.63CV, not CV/2, so the CV/2 option is wrong and the 'CV(1 - e⁻¹) after τ' option mismatches its stated time only if stated otherwise (here it states τ correctly, but the cleanly correct standard answer chosen is the 2τ statement). On energy: the source does work CV² total, the capacitor stores (1/2)CV², and exactly (1/2)CV² is dissipated as heat — so work done by source (CV²) equals twice (not half) the heat dissipated, making that option wrong. The unambiguous correct statement is q(2τ) = CV(1 - e⁻²).

A capacitor is initially uncharged in an RC circuit. Switch S1 is closed while S2 stays open, charging the capacitor through a resistor from a source of emf V. The circuit's time constant is τ. Which statement is correct?

Solution

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