Question

The dimensional formula of resistance is [ML²A^-2T^-3] and if heat is a form of energy, then the heat produced in a wire carrying an electric current which depends on the resistance (R), time (T) and electric current (I) using dimension analysis is 

(Here, symbols and notations carry their usual meanings)

(A) H = I²RT

(B) H = IRT

(C) H = 1/RT

(D) H = IT/R

Answer 1

Correct option is (A) H = I²RT

Let H = I^aR^bT^c

Write the dimensional formula of both part 

[ML²T^-2] = [A]^a [ML²A^-2T^-3]^b [T]^c

[ML²T^-2] = [M^bL^2bT^-3b+c A^a-2b] 

After comparing the power of left and right hand sides, we 

b = 1, -3b + c = -2

⇒ -3 x 1 + c = -2 

c = 1 

and a - 2b = 0, a

= 2b 

= 2 x 1 

= 2 

Substitute all the values in Eq. (i), we get 

H = I²RT