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

Yes, Kirchhoff's first rule (junction rule) is valid at each plate of the capacitor. Kirchhoff's first rule states that the sum of currents entering a junction is equal to the sum of currents leaving the junction.
At each plate of the capacitor, the conduction current \( I_c \) enters the plate and the displacement current \( I_d \) exits through the dielectric between the plates. Since the displacement current is equal in magnitude to the conduction current in the circuit, the total current entering and leaving each plate is the same. Thus, Kirchhoff's first rule holds at each plate.
Therefore, the junction rule is valid because the total current entering and leaving the plates is balanced by the conduction and displacement currents.