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  4. A wire of radius r and another wire of radius 2 r, both of same material and length are connected in series to each other. The combination is connected across a battery. The ratio of the heats produced in the two wires will be

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Q. A wire of radius $r$ and another wire of radius $2 r$, both of same material and length are connected in series to each other. The combination is connected across a battery. The ratio of the heats produced in the two wires will be

Current Electricity

Solution:

$H = I ^2 Rt$.
Here $R _1=\rho \frac{ l }{\pi r ^2}$ and $R _2=\rho \frac{1}{\pi(2 r )^2}$
That is, $R _1=4 R _2$.
Hence, $\frac{ H _1}{ H _2}=4$