Concept:The root mean square (RMS) value of alternating current is defined strictly by the thermal Joule heating effect in a pure resistor, which is independent of current direction.
Formula / Reaction:$$H = I_{\text{rms}}^2 R t = I_{\text{DC}}^2 R t$$
Solution:- Joule's heating law states \(P = I^2 R\). Because current is squared, heat dissipation is always positive regardless of instantaneous polarity.
- An AC of root-mean-square value \(I_{\text{rms}}\) produces the exact same average thermal power in a resistor as a steady DC of magnitude \(I_{\text{DC}} = I_{\text{rms}}\).
Why other options are incorrect:- Opt_A: Battery charging relies on chemical electrolysis, which requires unidirectional DC. AC produces zero net chemical deposition over a cycle.
- Opt_B: DC charges a capacitor to a constant state and then stops, whereas AC continuously charges and discharges it.
- Opt_D: An inductor opposes AC via inductive reactance \(X_L = 2\pi f L\), but offers zero reactance to steady DC.
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