Question

A capacitor consists of two parallel plates with an area of cross-section of 0.001 m², separated by a distance of 0.0001 m. If the voltage across the plates varies at the rate of 10⁸ V/s, then the value of displacement current through the capacitor is ______.

पर्याय

• 8.85 × 10⁻³ A

• 8.85 × 10⁻⁴ A

• 7.85 × 10⁻³ A

• 7.85 × 10⁻³ A

Answer 1

A capacitor consists of two parallel plates with an area of cross-section of 0.001 m², separated by a distance of 0.0001 m. If the voltage across the plates varies at the rate of 10⁸ V/s, then the value of displacement current through the capacitor is 8.85 × 10⁻³ A.

Explanation:

A = 0.001 m²

d = 0.0001 m

`(dv)/dt` = 10⁸ V/s

Displacement current, i_d = ?

i_d = `ε_0 (dØ)/dt`

= `ε_0 d/dt ((VA)/d)`

= `(ε_0 A)/d xx ((dV)/dt)`

= `(8.85 xx 10^-12 xx 0.001 xx 10^8)/0.0001`

= `(8.85 xx 10^-4 xx 10^-3)/10^-4`

= 8.85 × 10⁻³ A