Question

Assertion: An inductance and a resistance are connected in series with an AC circuit. In this circuit the current and the potential difference across the resistance lag behind the potential difference across the inductance by an angle $ \pi /2 $ .
Reason: In L-R circuit voltage leads the current by phase angle which depends on the value of inductance and resistance both.
A) If both the assertion and reason are true and the reason is a true explanation of the assertion.
B) If both the assertion and reason are true but the reason is not true the correct explanation of the assertion.
C) If the assertion is true but reason false
D) If both the assertion and reason are false.

Answer 1

Hint The main function of an AC source is to alter the supply voltage in a circuit in a varying form which also varies the currents and voltages across the elements of the circuit with time. An inductor when initially uncharged will avoid current from flowing in the circuit since it wouldn’t want the magnetic flux to change through it because of Lenz’s law.

Complete step by step answer
When an AC voltage is applied to an LR circuit, the current and the voltage do not peak at the same time. The time lag between voltage and current spike is expressed in degrees which are also called the phase difference. The phase difference $ \phi \leqslant 90^\circ $
Since the inductor will always try to suppress the change in current in the circuit, the potential drop across the resistor lags behind the potential drop across the inductor by a phase angle of $ \pi /2 $ so the assertion is correct.
The phase angle of the LR circuit is calculated using
 $ \Rightarrow \tan \phi = \dfrac{{{X_L}}}{R} $ where $ {X_L} $ is the inductive reactance and $ R $ is the resistance of the circuit. Since the phase angle depends on both the inductance and resistance of the circuit the reason statement is also correct.
However, the reason is not the correct reason for the assertion because the phase angle difference between the current in the circuit and the potential drop across the resistor will have a phase difference of $ \pi /2 $ regardless of the value of the inductance or resistance in the circuit while the net potential difference which is mentioned in the reason statement depends on the resistor and the inductor.
So option (B) is the correct choice.

Note
In the reason statement, since it only mentions the voltage of the L-R circuit, we must consider it to be the net voltage of the circuit which is the resultant of the voltage drop across the resistor and the inductor. While the assertion and the reason both are correct, the net potential does lead the current but it is not always by $ \pi /2 $ .