The heat generated in a circuit is dependent upon the resistance, current and time for which the current is flown. If the error in measuring the above are 1%, 2% and 1% respectively. The maximum error in measuring the heat is :
Question
The heat generated in a circuit is dependent upon the resistance, current and time for which the current is flown. If the error in measuring the above are 1%, 2% and 1% respectively. The maximum error in measuring the heat is :
Solution
The heat generated in a circuit (H) is given by Joule's law, which states that H = I^2RT, where I is the current, R is the resistance, and T is the time.
The maximum error in a product of quantities is given by the sum of the relative errors of those quantities.
The relative error in the measurement of I is 2%, in R is 1%, and in T is 1%. However, because the current I is squared in the formula, its relative error is doubled in the calculation of the heat, making it 4%.
Therefore, the maximum error in the measurement of the heat is 4% (from I^2) + 1% (from R) + 1% (from T) = 6%.
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