Capacitor Current

Electricity and Magnetism Level 2

Amy connects a pair of metal plates to an electric circuit made up of a battery, a switch, and a resistor. The metal plates are separated by a small distance by air.

What happens when she closes the switch?

Constant current flows in the circuit Current flows for a short while, and then drops to zero The circuit is open, so no current flows

2 solutions

Steven Chase
Nov 6, 2017

Capacitor differential equation:

$i = C \frac{dV}{dt}$

Here, the voltage is essentially a step, so the current in the beginning is either infinite or undefined. However, in reality, there will be some resistance in the circuit, as well as some parasitic inductance. These additional elements prevent the infinities from arising. In DC steady-state, the derivative of the voltage across the capacitor is zero by definition, and so is the current.

Peyton Bell
Nov 6, 2017

After Amy closes the switch, current will flow through the circuit until the capacitor (the metal plates) becomes fully charged. As the charge on the plates increases, resistance of the capacitor also increases, and therefore the resistance of the circuit increases, causing overall current to decrease. After some time, the resistance in the capacitor will be so great that current stops flowing altogether.

Capacitor Current

2 solutions

0 pending reports