A constant voltage source is applied between the two ends of a wire. If the length of the wire is doubled and the radius remains the same, then the rate of heat developed in the wire ________.

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SSC JE Electrical 11 Oct 2023 Shift 3 Official Paper-I
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  1. will be 4 times
  2. will be zero
  3. will be halved
  4. will remain the same

Answer (Detailed Solution Below)

Option 3 : will be halved
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Detailed Solution

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Concept

The heat developed in the wire is given by:

\(H=P\times t=(I^2R)\times t\)

The resistance is given by:

\(R={\rho L\over A}\)

where, H = Developed heat

I = Current

R = Resistance

L = Length of wire

Calculation

Given, L2 = 2L1 and A2 = A1

\({R_2\over R_1}={L_2\over L_1}\times {A_1\over A_2}\)

\(R_2=2R_1\)

If resistance becomes twice, then the current will become half of the initial value.

\(I_2=0.5I_1\)

\({H_2\over H_1}=({I_2\over I_1})^2\times {R_2\over R_1}\)

\({H_2\over H_1}=({0.5I_1\over I_1})^2\times {2R_1\over R_1}\)

\(H_2=0.5H_1\)

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