Question

A heating coil is rated $100W,220V$. The coil is cut in half and two pieces are joined in parallel to the same source. Now what is the energy (in $\times {10}^{2}J$) liberated per second?

Answer 1

Let the resistance of heating coil is $R$.
$P=\frac{V^2}{R}\Rightarrow R=\frac{V^2}{P}=\frac{(220{)}^2}{100}$
Hence the resistance of each part is $R/2$
As they are join in parallel so equivalent resistance $R_{eq}=\frac{\left(\frac{R}{2}\right)\left(\frac{R}{2}\right)}{\frac{R}{2}+\frac{R}{2}}=\frac{R}{4}$
Energy liberated per second is the power dissipation.
Thus dissipated power $=\frac{V^2}{R_{eq}}=\frac{4(220{)}^2}{R}=\frac{4(220{)}^2\times 100}{(220{)}^2}=4\times {10}^{2}J$