Question

# 5.4.2 An air-filled parallel-plate capacitor has plates of 10-3 m² that are separated by a distance...

5.4.2 An air-filled parallel-plate capacitor has plates of 10-3 m² that are separated by a distance of 2 mm. If the capacitor is connected to a 50-V 1-MHz sinusoidal voltage source, calculate the magnitude of the displacement current, neglecting fringing.

The data which is provided in this problem is:

;

The capacitor is also connected to a 50-V, 1-Mhz sinusoidal voltage source so the voltage across the plates of the capacitor can also be written as:

.....(1)

where

and is given to be 1 MHz = .

thus .

The displacement current density is given by;

............(2)

where E(t) is the time-varying field between the plates of the capacitor.

But the electric field is also given as the gradient of the potential, thus

........(3)

but from equation 1 and 3, we get,

........(4)

substituting the value of field in equation (2) we get,

,

thus the current will be

substituting all the values and taking the magnitude, we get

69.5 mA.

1. The expression for displacement current is obtained from the maxwell equations.

2. Since air is present between the plates, thus, the permittivity of free space will be used.

Thanks.

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