A current i passes through a wire of length l | vedclass

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(A) The rate of heat generation is given by the electrical power $P = i^2 R$.We know that the resistance $R$ of a wire is given by $R = \rho \frac{l}{

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$\frac{i^2 l \rho}{\pi r^2}$

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(A) The rate of heat generation is given by the electrical power $P = i^2 R$.We know that the resistance $R$ of a wire is given by $R = \rho \frac{l}{A}$, where $A$ is the cross-sectional area.The area of the cross-section of the wire is $A = \pi r^2$.Substituting the value of $A$ into the resistance formula, we get $R = \frac{\rho l}{\pi r^2}$.Now, substituting $R$ into the power formula, we get $P = i^2 \left( \frac{\rho l}{\pi r^2} \right) = \frac{i^2 l \rho}{\pi r^2}$.

$A$ current $i$ passes through a wire of length $l$, radius of cross-section $r$ and resistivity $\rho$. The rate of heat generation is

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