Question 138 of 168

A uniform heating wire of resistance $36\Omega$ is connected across a potential difference of $240V.$ The wire is then cut into half and a potential difference of $240V$ is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be $1:x,$ where $x$ is

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Answer: 4

$P={V}^{2}/R$

${P}_{1}=\dfrac{{V}^{2}}{\dfrac{R}{2}}\Rightarrow {P}_{2}=\dfrac{{V}^{2}}{\dfrac{R}{2}}\Rightarrow {P}_{1}+{P}_{2}=\dfrac{4{V}^{2}}{R}$
Now
$\dfrac{{P}_{1}+{P}_{2}}{P}=\dfrac{\dfrac{4{V}^{2}}{R}}{\dfrac{{V}^{2}}{R}}=4$