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(B) The heat developed in a wire is given by the formula $H = \frac{V^2}{R} t$,where $V$ is the constant voltage,$R$ is the resistance,and $t$ is the

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both the length and the radius of the wire are doubled.

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(B) The heat developed in a wire is given by the formula $H = \frac{V^2}{R} t$,where $V$ is the constant voltage,$R$ is the resistance,and $t$ is the time.For the heat $H$ to be doubled,the resistance $R$ must be halved.The resistance of a wire is given by $R = \rho \frac{l}{A} = \rho \frac{l}{\pi r^2}$,where $l$ is the length and $r$ is the radius.If both the length $l$ and the radius $r$ are doubled ($l' = 2l$ and $r' = 2r$),the new resistance $R'$ becomes:$R' = \rho \frac{2l}{\pi (2r)^2} = \rho \frac{2l}{4\pi r^2} = \frac{1}{2} \left( \rho \frac{l}{\pi r^2} \right) = \frac{R}{2}$.Since the resistance $R$ is halved,the heat developed $H$ will be doubled.

$A$ constant voltage is applied between the two ends of a uniform metallic wire. Some heat is developed in it. The heat developed is doubled if

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