Question

What capacitance, in μF, has its potential difference increasing at $1.0\times {10}^6\mathrm{V}/\mathrm{s}$when the displacement current in the capacitor is $1\mathrm{A}$?

Short answer

Required capacitance is $1\mu F$

Step-by-step solution

Given Information:

We been given that the rate of change of potential difference is $\frac{d{v}_c}{dt}=1.0\times {10}^6\mathrm{V}/\mathrm{s}$

Displacement Current = $I_d$= $1A$

Solving:

Relation for Displacement current against rate of change of potential difference is given by:

$I_d=c\left(\frac{d{v}_c}{dt}\right)$Equation

Also we been given:

$\frac{d{v}_c}{dt}=1.0\times {10}^6\mathrm{V}/\mathrm{s}$

Getting the value of c from Equation 1:

$c=\frac{I_d}{\left(\frac{d{v}_c}{dt}\right)}$

Putting the values:

$c=\frac{1.0}{1.0\times {10}^6}$

$c=1.0\times {10}^{-6}\mathrm{F}$

Therefore, The required value of capacitance is $1\mu F$