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

Question

For an electric dipole in a non-uniform electric field with dipole moment parallel to direction of the field, the force $F$ and torque $\tau$ on the dipole respectively are __________. Fill in the blank with the correct answer from the options given below.

Answer 1

Step 1: Understanding the Concept:
In AC circuits, different components cause a phase shift between the applied voltage (EMF) and the resulting current.
1. Purely Inductive ($L$): Current lags EMF by $\pi/2$ ($90^\circ$).
2. Purely Capacitive ($C$): EMF lags current by $\pi/2$ ($90^\circ$).
3. Resistive-Inductive ($RL$): Current lags EMF by an angle $\phi$ where $0<\phi<\pi/2$.
4. Resistive-Capacitive ($RC$): EMF lags current by an angle $\phi$ where $0<\phi<\pi/2$.
The phase angle $\phi$ is given by $\tan \phi = \frac{X}{R}$.
Step 2: Detailed Explanation:
Let's match each condition from List-I:

A. Current lags EMF by $\pi/4$:
"Lags" indicates an inductive component. Since the angle is $\pi/4$ (not $\pi/2$), resistance must also be present.
This corresponds to an A.C. circuit with resistance and inductance in series (II).

B. EMF lags current by $\pi/4$:
EMF lagging current (or current leading EMF) indicates a capacitive component. Since the angle is $\pi/4$, resistance is present.
This corresponds to an A.C. circuit with resistance and capacitor in series (IV).

C. Current lags EMF by $\pi/2$:
A full $\pi/2$ phase lag of current is the signature of a purely inductive circuit (I).

D. EMF lags current by $\pi/2$:
A full $\pi/2$ phase lag of EMF is the signature of a purely capacitive circuit (III).

Matching them together: A-II, B-IV, C-I, D-III.
Step 3: Final Answer:
The matching results in the sequence A-II, B-IV, C-I, D-III, which is option (B).

Show Hint

The Correct Option is B

Solution and Explanation

Top Questions on The Electric Field Due to an Electric Dipole

Questions Asked in CUET (UG) exam

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