Parallel AC circuit

Problem statement

In the circuit shown, the ammeter reading, which is the RMS value of the current through the capacitor, is $[[Ic]]$ A. The circuit has three branches in parallel connected to the generator $E$: one with $R_1$ and $R_2$ in series, another with the inductors $L_1$ and $L_2$ in series, and another with the ammeter and the capacitor $C$ in series.

Data: $R_1 = [[R1]]\ \Omega$, $R_2 = [[R2]]\ \Omega$, $X_{L1} = [[XL1]]\ \Omega$, $X_{L2} = [[XL2]]\ \Omega$, $X_C = [[XC]]\ \Omega$.

Calculate:

a) (0.4 marks) The RMS value of the electromotive force $E$.

b) (0.3 marks) The RMS value of the current through the resistors.

c) (0.3 marks) The RMS value of the current through the inductors.

d) (0.6 marks) Active, reactive and apparent power delivered by the generator $E$.

e) (0.4 marks) The RMS value of the current through the generator $E$.

Source: Madrid university entrance exam (PAU, Spain) · 2025-2026 · Ordinary session · Technology and Engineering · Question 4.1. Official exam set by the public universities of the Community of Madrid, to whom it belongs; translated from Spanish and reproduced with its source in order to explain it for teaching purposes.