Question

Match List-I with List-II: 

List-I	List-II
A. The current lags behind the e.m.f. by \( \frac{\pi}{4} \) in phase	I. A.C. circuit containing only an inductor
B. The e.m.f. lags behind the current by \( \frac{\pi}{4} \) in phase	II. A.C. circuit with resistance and inductance in series
C. The current lags behind the e.m.f. in phase by \( \frac{\pi}{2} \)	III. A.C. circuit containing only a capacitor
D. The e.m.f. lags behind the current in phase by \( \frac{\pi}{2} \)	IV. A.C. circuit with resistance and capacitor in series

• A. A-I, B-III, C-IV, D-II
• B. A-II, B-IV, C-I, D-III
• C. A-II, B-III, C-IV, D-I
• D. A-IV, B-II, C-I, D-III

Hint:

In pure inductor, current lags voltage by \(\frac{\pi}{2}\). In pure capacitor, current leads voltage by \(\frac{\pi}{2}\).

Answer 1

The Correct Option is B

Concept:
In A.C. circuits, the phase relation between current and voltage depends on the circuit element. For inductor: \[ \text{Current lags voltage} \] For capacitor: \[ \text{Current leads voltage} \]

Step 1: Match pure inductor.
In a pure inductive circuit, current lags behind e.m.f. by: \[ \frac{\pi}{2} \] So: \[ C \rightarrow I \]

Step 2: Match pure capacitor.
In a pure capacitive circuit, current leads e.m.f. by: \[ \frac{\pi}{2} \] This means e.m.f. lags behind current by: \[ \frac{\pi}{2} \] So: \[ D \rightarrow III \]

Step 3: Match \(R-L\) series circuit.
In an \(R-L\) series circuit, current lags behind e.m.f. by an angle between \(0\) and \(\frac{\pi}{2}\). Here, the given angle is: \[ \frac{\pi}{4} \] So: \[ A \rightarrow II \]

Step 4: Match \(R-C\) series circuit.
In an \(R-C\) series circuit, current leads e.m.f. by an angle between \(0\) and \(\frac{\pi}{2}\). This means e.m.f. lags behind current by an angle such as: \[ \frac{\pi}{4} \] So: \[ B \rightarrow IV \]

Step 5: Final matching.
The correct matching is: \[ A-II,\quad B-IV,\quad C-I,\quad D-III \] Hence: \[ \boxed{\text{(B)}} \]