How will the amount of heat that is released in a conductor change if the resistance

| May 23, 2021 | education

How will the amount of heat that is released in a conductor change if the resistance is doubled at a constant current strength?

Given:

I1 = I2 = I – the current does not change;

R2 = 2 * R1 – the conductor resistance was doubled.

It is required to determine Q2 / Q1 – how the amount of heat that is released in the conductor will change.

The amount of released heat in the first case will be equal to:

Q1 = W1 * t = U1 * I1 * t = I1 * I1 * R1 * t = I1 ^ 2 * R1 * t = I ^ 2 * R1 * t, where t is a certain period of time.

The amount of released heat in the second case will be equal to:

Q2 = W2 * t = U ^ 2 * I ^ 2 * t = I ^ 2 * I ^ 2 * R ^ 2 * t = I2 ^ 2 * R ^ 2 * t = I ^ 2 * R ^ 2 * t.

Then:

Q2 / Q1 = (I ^ 2 * R ^ 2 * t) / (I ^ 2 * R1 * t) = R ^ 2 / R1 = (2 * R1) / R1 = 2, that is, it will increase by 2 times.

Answer: when the resistance of the conductor doubles, the amount of heat released will also double.



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