Question

Differentiate between conduction current and displacement current. A capacitor is connected across a source providing time-dependent current. Explain how the total current at an instant is the sum of conduction current and displacement current in the circuit at that instant.

Hint:

Displacement current is the "missing link" that allowed Maxwell to predict the existence of electromagnetic waves.

Answer 1

Difference Between Conduction Current and Displacement Current
1. Conduction Current:
- Conduction current is the current due to the actual flow of charge carriers such as electrons in a conductor.
- It occurs in materials like metals where free charges are available.
- It is given by:
I = n e A v_d
where n is number density, e is charge, A is cross-sectional area and v_d is drift velocity.
- It produces a magnetic field around the conductor.

2. Displacement Current:
- Displacement current is the current associated with a time-varying electric field.
- There is no actual movement of free charges through the dielectric.
- It was introduced by Maxwell to explain the continuity of current in a capacitor.
- It is given by:
I_d = ε₀ (dΦ_E / dt)
where Φ_E is electric flux and ε₀ is permittivity of free space.

Capacitor Connected to a Time-Dependent Source
When a capacitor is connected to an alternating or time-dependent current source:
- In the connecting wires, current flows due to movement of electrons. This is conduction current.
- Between the plates of the capacitor, there is no physical flow of charge across the dielectric. However, the electric field between the plates changes with time.
- This changing electric field gives rise to displacement current.

Total Current in the Circuit
At any instant:
- The conduction current in the wires equals the displacement current between the plates.
- This ensures continuity of current in the circuit.
Thus, the total current at any instant is effectively:
I_total = I_conduction + I_displacement
But in a charging capacitor circuit:
I_conduction = I_displacement
So the current remains the same throughout the circuit at that instant.

Conclusion:
Conduction current is due to real charge flow, while displacement current is due to changing electric field. In a capacitor circuit with time-varying current, both together maintain the continuity of current in the entire circuit.