Question 165: EM waves

Question

A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance $2.5 \mu \mathrm{~F}$. The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _________ $\mathrm{Vs}^{-1}$.

Accepted Answer

$$ \frac{dV}{dt} = \frac{I}{C} $$
Given that the displacement current is $$ I = 0.25 	imes 10^{-3} \, 	ext{A} $$ and the capacitance is $$ C = 2.5 	imes 10^{-6} \, 	ext{F}, $$ the rate of change of the potential difference is calculated as follows:
$$ \frac{dV}{dt} = \frac{0.25 	imes 10^{-3}}{2.5 	imes 10^{-6}} = \frac{0.25}{2.5} 	imes \frac{10^{-3}}{10^{-6}} = 0.1 	imes 10^3 = 100 \, 	ext{V/s}. $$
Thus, the magnitude of the rate of change of the potential difference is $$ 100 \, 	ext{V/s} $$.

EM waves

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