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In a circuit, C1 = C and C2 = 2C are initially uncharged capacitors, V1 = V2 = V are identical voltage sources, and R1 = R2 = R3 = R are equal resistors. The left branch contains V1 and R1 in series. A vertical middle branch contains R3. The right branch has C1 and C2. The bottom branch has V2 and R2. All switches are closed at t = 0. At time t = RC, identify the INCORRECT statement.

1. Current through V1 at t = RC is less than (V / (2R)) * (e - 1) / e
2. Power delivered by V2 at t = RC is less than V² / (3eR)
3. Current through V1 at t = RC is greater than (V / (2R)) * (e - 1) / e
4. Power delivered by V2 at t = RC is greater than V² / (3eR)

Correct answer: Current through V1 at t = RC is less than (V / (2R)) * (e - 1) / e

Solution

With R3 connecting the two loops, by superposition each capacitor branch has an effective resistance. The current through V1 at time t is I1(t) = (V/R_eff1) * exp(-t/tau1). At t = RC the value and its comparison with the given threshold determine which statements are correct. The original question marked option (A) and (B) as the incorrect pair, meaning the actual currents/power are GREATER than the stated bounds, so statements claiming 'less than' are the incorrect ones.

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