In a capactive circuit, the reactance of capacitor at frequency 'f' is ' $\mathrm{X}_{\mathrm{c}}{…

In a capactive circuit, the reactance of capacitor at frequency 'f' is ' $\mathrm{X}_{\mathrm{c}}{ }^{\prime}$. What will be its reactance at frequency $4 \mathrm{f} ?$
  1. $\frac{\mathrm{X}_{\mathrm{C}}}{2}$
  2. $\frac{X_{C}}{4}$
  3. $\frac{\mathrm{X}_{\mathrm{C}}}{8}$
  4. $X_{C}$

Solution

Capacitive reactance $\mathrm{X}_{\mathrm{c}}=\frac{1}{2 \pi \mathrm{fC}}$ $\begin{array}{l} \therefore \frac{\mathrm{X}_{\mathrm{C}}^{\prime}}{\mathrm{X}_{\mathrm{c}}}=\frac{\mathrm{f}}{\mathrm{f}^{\prime}}=\frac{1}{4} \\ \therefore \mathrm{X}_{\mathrm{c}}^{\prime}=\frac{\mathrm{X}_{\mathrm{c}}}{4} \end{array}$

Asked in: MHT CET 2020 (14 Oct Shift 2)

Practice more Alternating Current questions on Aicharya