Question

L, C and R represent the physical quantities inductance, capacitance and resistance respectively. Which of the following combinations have dimensions of frequency?
(a) 1RC
(b) RL
(c) 1√LC
(d) C/L.

Answer 1

First 3 Options are Valid

Explanation:

$R = ML^2T^-^3A^-^2$

$C = M^-^1L^-^2T^4A^2$

$L = ML^2T^-^2A^-^2$

Option (a)

$\frac {1}{RC} = \frac {ML^2T^-^3A^-^2}{M^-^1L^-^2T^4A^2}$

$\frac {1}{RC} = \frac {1}{[T]}$

                     $= T^-^1$

or $sec^-^1 or\ s^-^1$

Option (b)  

$\frac {R}{L} = \frac {ML^2T^-^3A^-^2}{ML^2T^-^2A^-^2}$

$\frac {R}{L} = T^-^1$

$or\ sec^-^1 or\ s^-^1$

Option (c)

$\frac {1}{\sqrt LC} = \frac {1}{ML^2T^-^2A^-^2 \times M^-^1L^-^2T^4A^2}$

                              = $\frac {1}{\sqrt T^2}$

                              = $\frac {1}{T} = T^-^1$

As they have same value of $T^-^1$