Question

A heater coil connected to a supply of a $220V$ is dissipating some power $p_1$. the coil cut into half and the two halves are connected in parallel. heater is now dissipates a power $P_2$.The ratio of power $P_1:P_2$ is:

• A. $2:1$
• B. $1:2$
• C. $1:4$
• D. $4:1$

Answer 1

Answer: (D)

$4:1$

Let resistance of coil is $R$

Power of coil is

$p_1=\frac{v^2}{R}=\frac{{\left(220\right)}^2}{R}$

If Resistance is half and both are connected in parallel the equivalent resistance is ,

$R_{eq}=\frac{\frac{R}{2}\times \frac{R}{2}}{\frac{R}{2}+\frac{R}{2}}=\frac{R}{4}$

$p_2=\frac{v^2}{R_{eq}}=\frac{{\left(220\right)}^2}{\left(\frac{R}{4}\right)}=4\times \frac{{\left(220\right)}^2}{R}=4p_1$

$4p_1=p_2$

$p_1:p_2=4:1$

Option (D) is correct option