Question

Choose the correct answer from the alternatives given.
In order establish an instantaneous displacement current of 1 mA in the space between the plates of 2 $\mu F$ parallel plate capacitor. the rate of change of potential difference is:

• A. $100V{5}^{-1}$
• B. $200V{5}^{-1}$
• C. $300V{5}^{-1}$
• D. $500V{5}^{-1}$

Answer 1

Answer: (D)

$500V{5}^{-1}$

Given:

The required displacement current is, $I_D=1mA={10}^{-3}A$

The capacitance of the two plates is, $C=2\mu F=2\times {10}^{-6}F$

To find: The rate of chnage of potential difference.

The displacement current of the capacitor is the same as the conduction current. It is given by:

$I_D=I_C=\frac{dq}{dt}$

The charge stored in a capacitor is:

$q=CV$

Substitute the value of charge in the equation of displacement current.

$I_D=\frac{d}{dt}CV$

$⟹I_D=C\frac{dV}{dt}$

The rate of chnge of potential difference will be:

$\frac{dV}{dt}=\frac{I_D}{C}$

$⟹\frac{{10}^{-3}}{2\times 10-6}=500V{s}^{-1}$

Therefore, applying a varying potential difference of $500V{s}^{-1}$ would produce a displacement current of the desired value.