Question

Deduce an expression for heat produced by an electric conductor using dimensional analysis which depends upon heat proportional to current time and resistance.

Answer 1

Answer:

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Explanation:

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Answer 2

Explanation:

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

HOPE IT HELPS!!