InterviewSolution
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InterviewSolution
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10. The heat produced in a wire carrying an electric currentdepends on the current, the resistance and the time.Assuming that the dependence is of the product of powerstype, guess an equation between these quantities usingdimensional analysis. The dimensional formula ofresistance is ML ^2I^-2 T^-3 and heat is a form of energy. |
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Answer» Heat energy produced = power * time duration = I² R t = V² t / R H = I^k R^m T^n Let us try to find the dimensions of current in known units.Force = charge * electric field = current * time * voltage /distance current = Force * distance / (time * voltage) = force * distance/(time * current * resistance) I = M L T⁻² * L / (T * I * R) = M L² T⁻³ I⁻¹ R⁻¹ I² = M L² T⁻³ R⁻¹ I = M^1/2 L T^-3/2 R^-1/2 M L² T⁻² R^0 = energy = I^k R^m T^n = M^k/2 L^k T^-3k/2 R^-k/2 * R^m * T^n Equating the powers of the units : k = 2 n = 1 m = 1 Hence, H = I^2 R T |
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