Question

Write one merit and one de-merit of alternating current in comparison of direct current. Obtain expression for following in a pure inductive alternating current circuit
i) Instantaneous value of current
ii) Reactance of circuit
iii) Peak value of current Draw curve for power in pure inductive circuit.

Answer 1

Advantage
The generation of AC is more economical than DC
Disadvantage
The peak value of AC is high. It is dangerous to work with AC $(I_0=\sqrt{2}I)$
Pure inductor
$V_0\sin \left(\omega t\right)-L\frac{di}{dt}=0$
$V_0\sin \left(\omega t\right)=L\frac{di}{dt}$
$\int \frac{V_0}{L}\sin \left(\omega t\right)dt=\int di$
$-\frac{V_0}{L\omega }\left[\cos \right(\omega t\left)\right]=i$
$-\frac{V_0}{X_L}\left[\sin (\frac{\pi }{2}-\omega t))\right]=i$
$-i_0\sin (\frac{\pi }{2}-\omega t)=i$
$i=i_0\sin (\omega t-\frac{\pi }{2})$
$\left(i\right)i_0=\frac{V_0}{X_L}=\frac{V_0}{\omega L}\leftarrow$peak

value of current
(ii) $X_L=\omega L\to$ inductive reactance
(iii) $i=i_0\sin (\omega t-\frac{\pi }{2})$ instantaneous value