Question

A coil in the heater consumes the power $P$. ​If it is cut into halves and joined in parallel, ​what power will it consume?​

• A. $P^2$
• B. $2P$
• C. $\frac{P}{2}$
• D. $4P$

Answer 1

The correct option is D $4P$

Let the individual resistances after cutting be $R_1$ and $R_2$.
Resistance is proportional to the length. Since length is halved, resistance will also become half.​
$R_1=R_2=\frac{R}{2}$​

​Equivalent resistance when these are connected in parallel is:​
$\frac{1}{R_{\text{eq}}}=\frac{1}{R_1}+\frac{1}{R_2}$
$\frac{1}{R_{\text{eq}}}=\frac{1}{\left(\frac{R}{2}\right)}+\frac{1}{\left(\frac{R}{2}\right)}$
$\frac{1}{R_{\text{eq}}}=\frac{2}{R}+\frac{2}{R}$
$R_{\text{eq.}}=\frac{R}{4}$​

​Power is given by: ​
$P^{{}^{\prime }}=\frac{V^2}{R_{\text{eq}}}$
$P^{{}^{\prime }}=\frac{V^2}{\left(\frac{R}{4}\right)}=\frac{4V^2}{R}$
$P^{{}^{\prime }}=4P$​