Question

In the following circuit, the 1 $\Omega$ resistor dissipates power P. If the resistor is replaced by 9 $\Omega$, the power dissipated in it is

• A. $P$
• B. $3P$
• C. $9P$
• D. $P/3$

Answer 1

The correct option is A $P$

Equivalent resistance in the circuit $=(3+1)=4\Omega$

By Ohm's law,

$10V=\left(4\Omega \right)\left(iAmpere\right)$

$i=2.5A$

Power through a resistance is given by $P=I^{2}R$

Power through $1\Omega ,$

$P_{1\Omega }=i^2\times 1=6.25W$

Given, $P_{1\Omega }=P$

When $1\Omega$ is replaced by $9\Omega$, equivalent resistance $=(3+9)=12\Omega$

By Ohm's law,

$10V=\left(12\Omega \right)\left(i^{\prime }Ampere\right)$

Current $i^{\prime }=\frac{10}{12}A$

Power dissipated through replaced resistor, $P_{9\Omega }=(\frac{10}{12}{)}^2\times 9=6.25=P_{1\Omega }=P$

Option A is correct.