A coil in the heater consumes power P on passing current. If it is cut into halves and joined in parallel, will it consume power?

A coil in the heater consumes power

P

on passing current. If it is cut into halves and joined in parallel, will it consume power is

4 P

.
It is given that the coil is cut into two pieces and hence the resistance of each piece turn out to be

\frac{R}{2}

.
The equivalent resistance of the parallel connection is given by,

\frac{1}{R_{P}} = \frac{1}{R_{1}} + \frac{1}{R_{2}}

\Rightarrow \frac{1}{R_{P}} = \frac{1}{\frac{R}{2}} + \frac{1}{\frac{R}{2}}

\Rightarrow \frac{1}{R_{P}} = \frac{2}{R} + \frac{2}{R}

\Rightarrow \frac{1}{R_{P}} = \frac{4}{R}

\Rightarrow R_{P} = \frac{R}{4}

Therefore, new power consumed when two halves of wire are joined in parallel connection is equal to,

P^{'} = \frac{V²}{R_{P}}

{\Rightarrow P}^{'} = \frac{V²}{\frac{R}{4}}

{\Rightarrow P}^{'} = 4 \frac{V²}{R}

{\Rightarrow P}^{'} = 4 P

Hence, the new power is four times the old power when the wire is cut into two halves and joined parallelly.

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