JEE MainPhysicsUnits and Dimensions
If L , C , and R represent self-inductance, capacitance, and resistance respectively, which of the following combinations represents a dimensionless quantity?
Options
- AL R^2 C
- BL^2 R C
- CR^2 L C
- DL R C^2
Correct answer
A. L R^2 C
Step-by-step solution
The time constant of an RL circuit is given by ₁ = L R , which has the dimension of time [T] . The time constant of an RC circuit is given by ₂ = CR , which also has the dimension of time [T] . Taking the ratio of these two time constants yields a dimensionless quantity: ₁ ₂ = L R CR = L R^2 C Thus, the combination L R^2 C has no dimensions. Answer: L R^2 C