In the given circuit, the value of capacitor C that makes current I = 0 is ____________ μF.

Concept:

• It is given that the current flowing in the circuit is zero.
• This can happen only when the impedance of the circuit is infinite. 
• The given circuit is closed which means to get infinite impedance the denominator part of the impedance must be zero.
• That means the denominator of the impedance of the parallel sub-circuit is zero.

Application:

Given: ω = 5k rad/sec

Z = j5 || (j5 - j/ωC)

$Z=\frac{j5\times (j5-\frac{j}{\omega C})}{j5+j5-\frac{j}{\omega C}}$

By equating the denominator to zero, we get

$j10-\frac{j}{\omega C}=0$

$C=\frac{1}{10\omega }=\frac{1}{10\times 5000}F$

C = 20 × 10^-6 F 

∴ The value of C = 20 μF.