Question:
The displacement current flows through a capacitor when the voltage across its plates
The displacement current flows through a capacitor when the voltage across its plates
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Remember that displacement current behaves exactly like conduction current in terms of completing the circuit loop. Since a capacitor blocks steady DC (where voltage is constant) but allows AC (where voltage is continuously changing), displacement current only exists when the electric field (and hence the voltage) is changing with time.
Updated On: May 28, 2026
- becomes zero
- is increasing with time
- is decreasing with time
- attains a constant value
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Question:
The question asks under what conditions a displacement current flows through a parallel plate capacitor, based on the behavior of the voltage across its plates.
Step 2: Key Formula or Approach:
The displacement current \( I_d \) inside a capacitor of capacitance \( C \) is related to the time-varying electric flux \( \Phi_E \), which in turn depends on the voltage \( V(t) \) across its plates:
\[ I_d = \varepsilon_0 \frac{d\Phi_E}{dt} \]
Since \( E = \frac{V}{d} \) and \( \Phi_E = E A = \frac{V A}{d} \):
\[ I_d = \varepsilon_0 \frac{A}{d} \frac{dV}{dt} = C \frac{dV}{dt} \]
Thus, the displacement current is directly proportional to the rate of change of the voltage \( \frac{dV}{dt} \).
Step 3: Detailed Explanation:
From the relation \( I_d = C \frac{dV}{dt} \):
- If the voltage \( V \) is constant with time, then \( \frac{dV}{dt} = 0 \), and the displacement current is zero.
- If the voltage \( V \) is increasing with time, then \( \frac{dV}{dt} > 0 \), resulting in a positive, non-zero displacement current flowing through the capacitor. Thus, option (B) is correct.
- If the voltage \( V \) is decreasing with time, then \( \frac{dV}{dt} < 0 \), resulting in a negative, non-zero displacement current flowing through the capacitor (current in the reverse direction). Thus, option (C) is correct.
Therefore, a displacement current flows whenever the voltage across the capacitor is changing with time, i.e., when it is either increasing or decreasing.
Step 4: Final Answer:
The displacement current flows when the voltage is increasing with time (option B) or decreasing with time (option C).
The question asks under what conditions a displacement current flows through a parallel plate capacitor, based on the behavior of the voltage across its plates.
Step 2: Key Formula or Approach:
The displacement current \( I_d \) inside a capacitor of capacitance \( C \) is related to the time-varying electric flux \( \Phi_E \), which in turn depends on the voltage \( V(t) \) across its plates:
\[ I_d = \varepsilon_0 \frac{d\Phi_E}{dt} \]
Since \( E = \frac{V}{d} \) and \( \Phi_E = E A = \frac{V A}{d} \):
\[ I_d = \varepsilon_0 \frac{A}{d} \frac{dV}{dt} = C \frac{dV}{dt} \]
Thus, the displacement current is directly proportional to the rate of change of the voltage \( \frac{dV}{dt} \).
Step 3: Detailed Explanation:
From the relation \( I_d = C \frac{dV}{dt} \):
- If the voltage \( V \) is constant with time, then \( \frac{dV}{dt} = 0 \), and the displacement current is zero.
- If the voltage \( V \) is increasing with time, then \( \frac{dV}{dt} > 0 \), resulting in a positive, non-zero displacement current flowing through the capacitor. Thus, option (B) is correct.
- If the voltage \( V \) is decreasing with time, then \( \frac{dV}{dt} < 0 \), resulting in a negative, non-zero displacement current flowing through the capacitor (current in the reverse direction). Thus, option (C) is correct.
Therefore, a displacement current flows whenever the voltage across the capacitor is changing with time, i.e., when it is either increasing or decreasing.
Step 4: Final Answer:
The displacement current flows when the voltage is increasing with time (option B) or decreasing with time (option C).
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