Question 22: AC fundamentals

Question

What should be the value of the inductance of the coil which is to be connected to 220 V , 50 Hz supply so that maximum current of $3 \sqrt{2} A$ flows through the circuit ?

Accepted Answer

Supply voltage (rms)
$$V_{\rm rms}=220\rm\ V\quad\Longrightarrow\quad V_{\rm max}=V_{\rm rms}\sqrt2=220\sqrt2\;V$$
Given peak current
$$I_{\rm max}=3\sqrt2\;A$$
Inductive reactance
$$X_L=\frac{V_{\rm max}}{I_{\rm max}}      =\frac{220\sqrt2}{3\sqrt2}      =\frac{220}{3}\;\Omega$$
Relate $X_L$ to $L$ at $f=50$Ã¢ÂÂHz
$$X_L=2\pi f\,L      \quad\Longrightarrow\quad      L=\frac{X_L}{2\pi f}      =\frac{\frac{220}{3}}{2\pi\cdot50}      =\frac{220}{3\cdot100\pi}      =\frac{11}{15\pi}\;H$$
So the correct choice is Option C:
L = $\displaystyle\frac{11}{15\pi}$ H.

Answer

$L=\left(\frac{22}{15}\right) H$

Answer

$L=\left(\frac{15}{11 \pi}\right) H$

Answer

$L=\left(\frac{11}{15 \pi}\right) H$

Answer

$L=\left(\frac{22}{15} \sqrt{2}\right) H$

AC fundamentals

What should be the value of the inductance of the coil which is to be connected to 220 V , 50 Hz supply so that maximum current of 3 \sqrt{2} A flows through the circuit ?

Choose the correct answer: