A current of 1 A is used to charge a parallel plate capacitor with square plates.If the area of each plate is 0.6 m² the displacement current through a 0.3 m² area wholly between the capacitor plates and parallel to them is:

Question

Quizplus · Accepted Answer

The displacement current can be calculated using the formula:

I_d = ε_0 A (dV/dt)

where ε_0 is the permittivity of free space, A is the area of the surface through which the current passes, and (dV/dt) is the rate of change of voltage.

In this case, the area of the surface is given as 0.3 m^2 (0.3m x 1m), and the rate of change of voltage is equal to the current divided by the capacitance of the plates.

Since the plates are parallel and have equal area, the capacitance can be calculated using the formula:

C = ε_0 A / d

where d is the separation between the plates.

In this case, the separation is not given, but we can assume it is small compared to the dimensions of the plates (i.e. we can assume a parallel plate capacitor approximation). Therefore, we can use d = 0.6 mm = 0.0006 m.

Plugging in values, we get:

C = ε_0 A / d = (8.85 x 10^-12 F/m) x (0.6 m x 0.6 m) / 0.0006 m = 5.31 x 10^-9 F

Now we can calculate the rate of change of voltage:

(dV/dt) = I / C = 1 A / 5.31 x 10^-9 F = 1.88 x 10^8 V/s

Finally, plugging back into the displacement current formula:

I_d = ε_0 A (dV/dt) = (8.85 x 10^-12 F/m) x (0.3 m x 1 m) x (1.88 x 10^8 V/s) = 0.5 A

Therefore, the displacement current through the 0.3 m^2 area between the capacitor plates is 0.5 A.

A Current of 1 a Is Used to Charge a Parallel