# A uniform wire when directly connected along a 220 v line produces h heat per second .if the wire is divided into n parts then the heat produced per second will be ?

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by shreedevis99

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by shreedevis99

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It is not clear how one of the n segments is connected with the voltage 220V. So I give two possibilities.

Resistance of a uniform wire of cross sectional area A and length L = R = ρL/A

Power dissipated by a resistance R = P = V² / R = I² R , V = 220 V

Heat produced by the wire = power * duration = H = V² T /R = I² R T

1) When the entire wire of length L is connected across V = 220 V, the it produces a heat energy of H. In the same configuration, one of the n segments of length L/n has resistance R₁ = R/n. The current flowing through this segment is same as total current I.

Hence heat produced in this segment is = I²R₁ = I²(R/n) T = H/n

2) When one segment of the n segments is connected across voltage V = 220 V,

then heat produced is = V² T / R₁ = n V² T / R.

So heat produced in one segment is n times that produced by entire wire.

Resistance of a uniform wire of cross sectional area A and length L = R = ρL/A

Power dissipated by a resistance R = P = V² / R = I² R , V = 220 V

Heat produced by the wire = power * duration = H = V² T /R = I² R T

1) When the entire wire of length L is connected across V = 220 V, the it produces a heat energy of H. In the same configuration, one of the n segments of length L/n has resistance R₁ = R/n. The current flowing through this segment is same as total current I.

Hence heat produced in this segment is = I²R₁ = I²(R/n) T = H/n

2) When one segment of the n segments is connected across voltage V = 220 V,

then heat produced is = V² T / R₁ = n V² T / R.

So heat produced in one segment is n times that produced by entire wire.