Question
A resistor and an inductor are connected to an $$ac$$ supply of $$120\,V$$ and $$50\,Hz.$$ The current in the circuit is $$3\,A.$$ If the power consumed in the circuit is $$108\,W,$$ then the resistance in the circuit is
A.
$$12\,\Omega $$
B.
$$40\,\Omega $$
C.
$$\sqrt {\left( {52 \times 25} \right)} \,\Omega $$
D.
$$360\,\Omega $$
Answer :
$$12\,\Omega $$
Solution :
In an $$ac$$ circuit, a pure indcutor does not consume any power. Therefore, power is consumed by the resistor only.
$$\eqalign{
& \therefore P = I_v^2R \cr
& {\text{or}}\,\,108 = {\left( 3 \right)^2}R\,\,{\text{or}}\,\,R = 12\,\Omega \cr} $$