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A uniform heating wire of resistance

Question:

A uniform heating wire of resistance $36 \Omega$ is connected across a potential difference of $240 \mathrm{~V}$. The wire is then cut into half and potential difference of $240 \mathrm{~V}$ 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 $1: \mathrm{x}$, where $\mathrm{x}$ is..........

Solution:

First case $\mathrm{P}_{1}=\frac{\mathrm{V}^{2}}{\mathrm{R}}=\frac{(240)^{2}}{36}$

Second case Resistance of each half $=18 \Omega$

$\mathrm{P}_{2}=\frac{(240)^{2}}{18}+\frac{(240)^{2}}{18}=\frac{(240)^{2}}{9}$

$\frac{\mathrm{P}_{1}}{\mathrm{P}_{2}}=\frac{1}{4}$

$x=4.00$

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