If R and L denote resistance and inductance of a material, then the dimension of L R will be:

Step-by-step solution

The dimension of resistance R is given by V = IR , so [R] = [V][I]⁻¹ . Since V = W/q , [V] = [M L^2 T⁻²][A T]⁻¹ = [M L^2 T⁻³ A⁻¹] . Thus, [R] = [M L^2 T⁻³ A⁻²] . The dimension of inductance L is given by V = L(dI/dt) , so [L] = [V][T][I]⁻¹ = [M L^2 T⁻³ A⁻¹][T][A]⁻¹ = [M L^2 T⁻² A⁻²] . The dimension of the product LR is [L][R] = [M L^2 T⁻² A⁻²] [M L^2 T⁻³ A⁻²] = [M^2 L^4 T⁻⁵ A⁻⁴] . Answer: M^2 L^4 T⁻⁵ A⁻⁴