A uniform heating wire of resistance 36 Ω 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...
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Solution
First case
$$
P_1=\frac{V^2}{R}=\frac{(240)^2}{36}
$$
Second case Resistance of each half $=18 \Omega$
$$
\begin{aligned}
& P_2=\frac{(240)^2}{18}+\frac{(240)^2}{18}=\frac{(240)^2}{9} \\
& \frac{P_1}{P_2}=\frac{1}{4} \\
& x=4.00
\end{aligned}
$$
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