Question

A $220V,50Hz$ ac generator is connected to an inductor and a $50\Omega$ resistance in series. The current in the circuit is $1.0A$. What is the PD across inductor?

• A. $102.2V$
• B. $186.4V$
• C. $214V$
• D. $170V$

Answer 1

The correct option is C $214V$

$V_{rms}=220V$

$f=50Hz$

$R=50\Omega$

$I=4A$

$L=?$

$I=\frac{V}{\sqrt{R^2+(X_L{)}^2}}$

$1=\frac{V}{\sqrt{R^2+(2\pi \times 50\times L{)}^2}}$

$2500+{100}^2{\pi }^2{L}^2=48400$

$\therefore L^2=0.46$

$L=0.68H$

$V_{rms}\left(acrossL\right)=I{X}_L=1\times 2\pi \times 50\times 0.68=213.6Volt\approx 214Volt$