A uniform heating wire of resistance $36\, \Omega$ is connected across a potential difference of $240\, {V}$ The wire is then cut into half and potential difference of $240\, {V}$ 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 $1: {x}$, where ${x}$ is........... .
JEE MAIN 2021, Medium
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First case ${P}_{1}=\frac{{V}^{2}}{{R}}=\frac{(240)^{2}}{36}$
Second case Resistance of each half $=18 \,\Omega$
${P}_{2}=\frac{(240)^{2}}{18}+\frac{(240)^{2}}{18}=\frac{(240)^{2}}{9}$
$\frac{{P}_{1}}{{P}_{2}}=\frac{1}{4}$
${x}=4.00$
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