Question

A source of 220V is applied in an A.C. circuit. The value of resistance is $220\Omega$. Frequency & inductance are 50 Hz and 0.7 H, then wattless current is

• A. $0.5amp$
• B. $0.7amp$
• C. $1.0amp$
• D. none

Answer 1

Answer: (B)

$0.7amp$

$\Rightarrow R=2\Omega$

$\Rightarrow V_{rms}=220V$

$\Rightarrow V_{\circ }=220\sqrt{2}$

$\Rightarrow X_L=WL=100\pi \times 0.7$

$\Rightarrow 100\frac{22}{7}\times \frac{7}{10}=220\Omega$

$\therefore z=220\sqrt{3}$

also $\tan \varphi =\frac{V_L}{R}=1$

$\varphi ={45}^{\circ }$

$\therefore$ wattless current$=i_{\circ }\sin \varphi$

$=\frac{220\sqrt{3}}{220\sqrt{2}}\sin {45}^{\circ }$

$=\frac{1}{\sqrt{2}}=0.7A$

so we get $0.7A$

Hence option$B$ is correct.