Question

If R, X_L and X_C represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless

(1) R X_L X_c

(2) \(\frac{R}{\sqrt{X_LX_C}}\)

(3) \(\frac{R}{X_LX_C}\)

(4) \(R\frac{X_L}{X_C}\)

Answer 1

Correct option is (2) \(\frac{R}{\sqrt{X_LX_C}}\)

All three have same dimension therefore \(\frac{R}{\sqrt{X_LX_C}}\) is dimensionless.