If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

Solution

Physics sir · 3 steps

Write L and C in terms of R and time, and each option becomes a one-line check.

1. Two time constants. In an RC circuit the time constant is RC, and in an LR circuit it is L/R. Both have the dimension of time T.
2. Rewrite L and C. From these two results, [L] = [R] T and [C] = T/[R]. Put these into each option and see whether only T is left.

   Option	Substitute	Dimension
   (a) RC	R × T/R	T
   (b) L/R	(R T)/R	T
   (c) √LC	√(R T × T/R)	T
   (d) L/C	(R T)/(T/R)	R², not time

3. So. L/C has the dimension of resistance squared, [M² L⁴ T⁻⁶ A⁻⁴]. The answer is (d).

The idea to keep. Remember RC and L/R as time constants. Then [L] = R T and [C] = T/R, so any mix of L, C and R reduces to powers of R and T.

Answer from the NTA final answer key. Solution by PrepWiser.