An AC circuit consists of a series combination of circuit elements X and Y. The current is ahead of the voltage in phase by π/4. If element X is a pure resistor of 100Ω: (a) name the circuit element Y. (b) calculate the rms value of current, if the rms value of voltage is 141V. (c) what will happen if the AC source is replaced by a DC source?

As the current is ahead of the voltage in phase, the circuit is capacitive. Hence, Y has to be a capacitor.

The impedance Z of the series RC circuit is given by:
Z = √(R² + Xc²)
where R is the resistance and Xc is the capacitive reactance.

Given that the phase difference between current and voltage is π/4, we have:
Xc/R = tan(π/4) = 1
Xc = R = 100Ω

Therefore, the impedance is:
Z = √(R² + Xc²) = √(100² + 100²) = √(20000) = 100√2 Ω

The rms value of current is given by:
Irms = Vrms / Z = 141V / (100√2 Ω) ≈ 0.9987 A ≈ 1 A

If the AC source is replaced by a DC source, the capacitor will act as an open circuit after it is fully charged. Therefore, no current will flow through the circuit. The voltage across the resistor will be equal to the DC source voltage, while the voltage across the capacitor will be equal to the DC source voltage.