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  • Stuck here, help me understand: A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :

A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :

  • Option 1)

    Doubled

  • Option 2)

    Halved

  • Option 3)

    Unchanged

  • Option 4)

    Increased 8 times

 

Answers (2)

best_answer

As we learnt

Resistance formula -

R=\rho \frac{l}{A}=\frac{m}{ne^{2}\tau}\cdot \frac{l}{A}

- wherein

\rho = resistivity of material

n= Number of free electrons per unit volume.

 

 Heat=\frac{v^{2}}{R}

\frac{H_{1}}{H_{2}}=\frac{R_{2}}{R_{1}}=\frac{\rho l_{2}}{A_{2}\rho l_{1}/{A_{1} }}

    =\frac{l_{2}}{l_{1}}.\frac{A_{1}}{A_{2}}

=\frac{1}{2}*\frac{1}{4}=\frac{1}{8}

H_{2}=8H_{1}


Option 1)

Doubled

Option 2)

Halved

Option 3)

Unchanged

Option 4)

Increased 8 times

Posted by

Plabita

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