First slide

Electrical power

Question

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

Moderate

A

both the length and radius of the wire are halved
B

both the length and radius of the wire are doubled
C

the radius of the wire is doubled
D

the length of the wire is doubled

Solution

Heat developed $H = \frac{V^{2}}{R} \times t$
Heat developed will be doubled when .R is halved.
Further. $R = \frac{ρl}{A} = \frac{ρl}{{πr}^{2}}$
$∴ H = \frac{V^{2} \times {πr}^{2}}{ρl} \times t$
So, heat produced will be doubled when both the length and radius of the wire are doubled

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