In the following circuit, $1 \,\Omega$ resistor dissipates power $P$. If the resistor is replaced by $9 \,\Omega$, the power dissipated in it is
KVPY 2011, Medium
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(a)
From given circuit, if $i=$ circuit current, then
$V=i R_{ eq } \Rightarrow i=\frac{10}{4}=2.5 \,A$
So, power dissipated by circuit is
$P=i^2 R=(2.5)^2 \times 1=\frac{25}{4} W$
When $1 \,\Omega$ resistor is replaced by a $9 \,\Omega$ resistor, then power dissipated in $9\, \Omega$ resistor is
$P^{\prime}=\left(\frac{10}{12}\right)^2 \times(9)$
$=\frac{100 \times 9}{12 \times 12}=\frac{25}{4} \,W$
So, $P^{\prime}=P$
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