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In a series R1-R2-C circuit (R1 in series with a parallel combination of R2 and capacitor C) connected to a battery of EMF E, which of the following statements is INCORRECT a long time after the switch is closed?

1. The voltage drop across the capacitor equals E.
2. The current through the battery is E / (R1 + R2).
3. The energy stored in the capacitor is (1/2) * C * (R2 * E / (R1 + R2))².
4. The current through the capacitor is zero.

Correct answer: The voltage drop across the capacitor equals E.

Solution

At steady state, the capacitor is fully charged and no current flows through it. The circuit reduces to E in series with R1 and R2. Current through battery = E/(R1+R2). Voltage across R2 (= voltage across capacitor) = E*R2/(R1+R2), which is less than E (not equal to E). Therefore statement A is INCORRECT. Statements B, C, D are all correct.

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