The conduction current is the same as displacement current when the source is

Options

A. ac only
B. dc only
C. either ac or dc
D. neither dc nor ac

Answer

To determine when the conduction current is the same as the displacement current, we can analyze the situation using the concepts of capacitors and the nature of the currents involved.

### Step-by-Step Solution:

1. **Understanding Conduction and Displacement Current**:
- Conduction current is the actual flow of charge through a conductor.
- Displacement current is a concept introduced by Maxwell to account for changing electric fields in situations where there is no actual charge flow, such as in a capacitor.

2. **Capacitor Behavior**:
- In a capacitor, the relationship between charge (Q), capacitance (C), and voltage (V) is given by the equation:
\[ Q = C \cdot V \]
- The current (I) flowing through the capacitor can be expressed as:
\[ I = \frac{dQ}{dt} \]
- By substituting the expression for Q, we get:
\[ I = C \cdot \frac{dV}{dt} \]

3. **Analyzing Current with Constant Voltage**:
- If the voltage (V) across the capacitor is constant, then \( \frac{dV}{dt} = 0 \). This implies:
\[ I = C \cdot 0 = 0 \]
- Therefore, when the voltage is constant (like in a DC source), the conduction current is zero.

4. **Analyzing Current with Time-Varying Voltage**:
- In contrast, if the voltage across the capacitor is time-varying (as in an AC source), then \( \frac{dV}{dt} \) is not zero, and thus:
\[ I = C \cdot \frac{dV}{dt} \neq 0 \]
- In this case, the displacement current, which is defined as:
\[ I_d = \epsilon_0 \cdot \frac{dE}{dt} \]
where \( E \) is the electric field, also contributes and is non-zero.

5. **Conclusion**:
- The conduction current is equal to the displacement current when the source is an **AC voltage source**. This is because both currents are active and contribute to the total current in the circuit.

### Final Answer:
The conduction current is the same as the displacement current when the source is an **AC voltage source**.