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An AC voltage source (rms = 36 V, f = 50 Hz) is connected in a circuit with two identical resistors R1 = R2 = R and a capacitor C in parallel. Two ammeters A1 and A2 (negligible resistance) are also in the circuit. Measured currents: I1 = 5 A (through A1), I2 = 4 A (through A2). Which of the following statements is/are correct? (A) The current through R1 is 3 A. (B) The current through C is sqrt(13) A. (C) The phase angle between the current through A1 and the source is tan⁻¹(sqrt(13)/sqrt(12)). (D) The phase angle between the current through A2 and the source is tan⁻¹(sqrt(13)/3).

1. The current through R1 is 3 A
2. The current through C is sqrt(13) A
3. The phase angle between the current through A1 and source is tan⁻¹(sqrt(13)/sqrt(12))
4. The phase angle between the current through A2 and source is tan⁻¹(sqrt(13)/3)

Correct answer: The current through R1 is 3 A

Solution

Without the figure, the most common configuration: R1 is in series; R2 and C are in parallel; A1 measures total current (5A), A2 measures branch current through parallel combination (4A). Then I_R1 = I1 = 5A (if A1 is in series with R1)... This requires the figure. However from given data: I1=5A, I2=4A. If I_R1 and I2 are in quadrature (R1 in one branch, R2||C in another parallel branch): I1² = I_R1² + I2² doesn't work with integer solutions. Try I2 combines I_R2 and I_C: I_R2 and I_C perpendicular. From answer A: I_R1=3A. Then if I1 is total: I1² = I_R1² + I_remaining² -> 25 = 9 + I_rem² -> I_rem = 4 = I2. This is consistent. I2=4A is phasor sum of R2 and C branches. So I_R1=3A confirmed. Statement A is correct.

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