The displacement current is found

Options

A. between the plates of a condenser when it is being charged
B. between the plates of a condenser when it is being discharged
C. between the plates of a condenser when AC is applied to the condenser
D. in the above 1, 2, 3 cases

Answer

To solve the question regarding the displacement current, we will analyze the concept and its implications in different scenarios involving a capacitor (condenser).

### Step-by-Step Solution:

1. **Understanding Displacement Current**:
- Displacement current is a term introduced by James Clerk Maxwell to describe a current that can exist in regions where there is a changing electric field, even in the absence of actual charge flow. It is defined mathematically as:
\[ I_d = \epsilon_0 \frac{d\Phi_E}{dt} \]
where \( I_d \) is the displacement current, \( \epsilon_0 \) is the permittivity of free space, and \( \Phi_E \) is the electric flux.

2. **Charging a Capacitor**:
- When a capacitor is charged, an electric field builds up between its plates. Although there is no physical current flowing through the dielectric between the plates, there is a changing electric field, which gives rise to a displacement current. This can be observed by placing a magnetic needle nearby, which will deflect due to the magnetic field created by the displacement current.

3. **Discharging a Capacitor**:
- Similarly, when the capacitor discharges, the electric field between the plates decreases. This change in the electric field also produces a displacement current. Again, the magnetic needle will show deflection, indicating the presence of displacement current.

4. **Alternating Current (AC) in a Capacitor**:
- When an alternating current is applied to the capacitor, the electric field between the plates continuously changes direction and magnitude. This continuous change in the electric field results in a displacement current as well. The magnetic needle will again deflect, showing that displacement current is present.

5. **Conclusion**:
- In all three scenarios (charging, discharging, and applying AC), displacement current is indeed found between the plates of the capacitor. Therefore, the correct option that encompasses all these scenarios is option D, which states that displacement current is found in all three cases.

### Final Answer:
The displacement current is found in:
- 1. Between the plates of the capacitor when it is being charged.
- 2. Between the plates of the capacitor when it is being discharged.
- 3. Between the plates of the capacitor when alternating current is applied.

Thus, the correct option is **D** (all of the above).