Question

A wire when connected to 220V mains supply has power dissipation $P_1$. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is $P_2$. Then $P_2:P_1$ is

• A. 1
• B. 4
• C. 2
• D. 3

Answer 1

The correct option is B 4

Given: A wire when connected to $220V$ mains supply has power dissipation $P_1$. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is $P_2$.

To find $P_2:P_1$

Solution:

Let the resistance of the whole wire = $R$

We know,

$P_1=\frac{V^2}{R}$

Now after cutting the wire into two equal pieces the resistance of each piece = $\frac{R}{2}$

Equivalent resistance parallel combination of two $\frac{R}{2}$ resistors

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

Power dissipation becomes

$P_2=\frac{V^2}{\frac{R}{4}}⟹P_2=\frac{4V^2}{R}⟹P_2=4P_1⟹P_2:P_1=4$