Question

In case (a) above, is Kirchhoff's first rule (junction rule) valid at each plate of the capacitor? Explain.

Hint:

Kirchhoff's first rule is valid as long as the currents entering and leaving a junction (in this case, the plates of a capacitor) are balanced, including the contribution from the displacement current.

Answer 1

Kirchhoff's First Rule at Capacitor Plates

Kirchhoff's first rule, also termed the junction rule, asserts that the total current entering a junction equals the total current exiting. This principle is a consequence of electric charge conservation.

Application of Kirchhoff's First Rule to a Capacitor:

Each capacitor plate experiences two current types:

• Conduction Current (I_c): This current flows into the capacitor plate from the external circuit.
• Displacement Current (I_d): This current emerges through the dielectric between the plates, driven by a changing electric field.

The displacement current's magnitude equals the conduction current's magnitude within the circuit. Consequently, the total current entering and leaving each capacitor plate is balanced. Therefore, Kirchhoff's first rule is satisfied at each plate, as the incoming conduction current equals the outgoing displacement current.

Summary:

Kirchhoff's junction rule is thus applicable to each capacitor plate, with the conduction and displacement currents balancing each other to maintain equal incoming and outgoing total currents.