Question

A $40\mu F$ capacitor is connected to a $200V,50Hz$ ac supply. The RMS value of the current in the circuit is, nearly:

• A. $1.7A$
• B. $2.05A$
• C. $2.5A$
• D. $25.1A$

Answer 1

The correct option is C

$2.5A$

Step 1: Given Data

The capacitance of the capacitor $C=40\mu F=40\times {10}^{-6}F$

Voltage through the capacitor $V_{rms}=200V$

Frequency of the ac supply $f=50Hz$

Step 2: Calculate the Impedance

The impedance of a capacitor is given as,

$X_C=\frac{1}{\omega C}=\frac{1}{2\mathrm{\pi f}C}$

$\Rightarrow X_L=\frac{1}{2\mathrm{\pi }\times 50\times 40\times {10}^{-6}}$

Step 3: Calculate the Current

The RMS current through a capacitor is given as,

$I_{rms}=\frac{V_{rms}}{X_L}$

Upon substituting the values we get,

$I_{rms}=200\times 2\times 3.14\times 50\times 40\times {10}^{-6}$

$\Rightarrow I_{rms}=2.5A$

Hence, the correct answer is option (C).