Physics, asked by kabeerbulai, 1 year ago

The heat produced (H) in a wire carrying an electric current depends on the current, the resistance, and the time. Assuming that the dependence is of the product of powers type, guess an equation between these quantities using dimensional analysis. Heat is a form of energy

Answers

Answered by kvnmurty
74
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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