Question

A coil has resistance $30$ ohm and inductive reactance $20$ ohm at $50 \,Hz$ frequency. If an ac source, of $200$ volt, $100\, Hz$, is connected across the coil, the current in the coil will be

• A. 2.0 A
• B. 4.0 A
• C. 8.0 A
• D. $\frac{20}{\sqrt{13}}A$

Answer 1

Answer: (B)

4.0 A

Answer 2

$X _{ L }=2 \pi fL$
$X _{ L } \propto f$
$\frac{ X _{ L _{2}}}{ X _{ L _{1}}}=\frac{ f _{2}}{ f _{1}}$
$\Rightarrow X _{ L _{2}}=40 \,\Omega$
$R =30 \Omega$
$Z =\sqrt{(30)^{2}+(40)^{2}}=50 \,\Omega$
$I =\frac{ V }{ Z }=\frac{200}{50}$
$=4 \,A$