Question

In an $L-R$ series circuit, a siunsoidal voltage $v=v_0\sin \cot \omega$ is. It is given that $L=35mH$ and $R=11\Omega ,V_{ms}=220V,\frac{\omega }{2\pi }=50Hz$ and $\pi =\frac{22}{7}$. The amplitude of the current is:

• A. $2amp$
• B. $20amp$
• C. $200amp$
• D. $4amp$

Answer 1

The correct option is B $20amp$

$L=35$mH

$V=V_0\sin \omega t$

$V_{rms}=220V$

$W=2\pi V$

$2\pi \times 50=100\pi {\sec }^{-1}$

$T=V/Z$

$=\left(2V_{rms}\right)1/2(X{L}^2+R^2)1/2$

$=\left(2\right)1/2\times 220/\left[\right(100\pi \times 35\times {10}^{-3}{)}^2]1/2+{11}^2$

$=\left(2\right)1/2\times 220/\left[\right({10}^{-1}\times 22/7\times 35){]}^2+{11}^{1/2}$

$=\left(2\right)1/2\times 220/\left[\right(22\times 5/{10}^2){]}^2+121$

$=\left(2\right)1/2\times 220({11}^2+121)1/2$

$=\left(2\right)1/2\times 220/{11}^2+{11}^2$

$=\left(2\right)1/2/\left(2\right)1/2\times 220\times 11$

$=20A$

$20$Ampere.