Question

When a coil is connected to a $100$ $V$ DC supply, the current is $2$ $A$. When the same coil is connected to AC source $E=100\sqrt{2}\sin \omega t$, the current is $1$ $A$. Find the inductive reactance used in the circuit.

Answer 1

$R=\frac{V}{I}$

$\Rightarrow R=\frac{100}{2}$

$\Rightarrow R=\frac{100}{2}$

$\Rightarrow R=50$ $\Omega$

$\frac{100}{1A}=Z=\frac{V}{I}$

$\sqrt{R^2+X^2}=100$

$\Rightarrow X^2={100}^2-{50}^2$

$\Rightarrow X=\sqrt{{100}^2-{50}^2}=\sqrt{7500}=50\sqrt{3}$

$\Rightarrow X=86.60$ $\Omega$