A parallel plate capacitor of capacitance \(20 μF\) is being charged by a voltage source whose potential is changing at the rate of \(3 V/s.\) The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively:

Question

If the plates of a parallel plate capacitor connected to a battery are moved close to each other, then
A. the charge stored in it, increases.
B. the energy stored in it, decreases.
C. its capacitance increases.
D. the ratio of charge to its potential remains the same.
E. the product of charge and voltage increases.
Choose the most appropriate answer from the options given below :

Answer 1

To solve this problem, we need to determine both the conduction current through the connecting wires and the displacement current through the plates of the capacitor. Let's start by understanding the two key concepts involved:

Conduction Current (\(I_c\)): This is the current that flows through the conductive wires connected to the capacitor. It is associated with the movement of real charges and is usually calculated using the capacitor charging formula.
Displacement Current (\(I_d\)): This is a concept introduced by Maxwell, which accounts for the changing electric field between the plates of a capacitor when it is being charged or discharged. It's not a current in the traditional sense, as it does not involve the movement of real charges, but it is equal in magnitude to the conduction current when the system is in a steady state.

Given:

Capacitance of the capacitor, \( C = 20 \, \mu F \) (microfarads)
Rate of change of voltage, \( \frac{dV}{dt} = 3 \, V/s \)

We know from the theory of capacitors that the conduction current, \( I_c \), and the displacement current, \( I_d \), through the capacitor are given by the formula:

I = C \frac{dV}{dt}

Substituting the given values into the formula:

I = 20 \times 10^{-6} \times 3 \, A

Calculating:

I = 60 \times 10^{-6} \, A or I = 60 \,\mu A

Therefore, both the conduction current (I_c) and the displacement current (I_d) are 60 \,\mu A each.

Thus, the correct answer is (\text{60 } \mu A, \text{ 60 } \mu A).

Conclusion: Since the potential across the capacitor is changing, both the conduction and displacement currents will have the same magnitude, as derived above.

Correct Answer: \(60 \,\mu A, 60 \,\mu A\)

Answer 2