Question

which of the following dimensions are same that of the time
a) L/R
b) C/L
c) LC
d) R/L

Answer 1

Answer:

(a). The dimension of the $\dfrac{L}{R}$ is same of the time dimension.

Explanation:

We know that,

The dimension formula of R is

$R = [ML^2T^{-3}A^{-2}]$

The dimension formula of L is

$L = [ML^2T^{-2}A^{-2}]$

The dimension formula of C is

$C = [M^{-1}L^{-2}T^{-4}A^{2}]$

(a). The dimension formula of $\dfrac{L}{R}$ is

$\dfrac{L}{R}=\dfrac{ [ML^2T^{-2}A^{-2}]}{ [ML^2T^{-3}A^{-2}]}$

$\dfrac{L}{R}=T$

(b). The dimension formula of $\dfrac{C}{L}$ is

$\dfrac{C}{L}=\dfrac{ [M^{-1}L^{-2}T^{-4}A^{2}]}{ [ML^2T^{-2}A^{-2}]}$

$\dfrac{C}{L}=M^{-2}L^{-4}T^{-2}A^{4}$

(c).The dimension formula of LC is

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

$LC=T^{-2}$

(d). The dimension formula of $\dfrac{R}{L}$ is

$\dfrac{R}{L}=\dfrac{ [ML^2T^{-3}A^{-2}]}{ [ML^2T^{-2}A^{-2}]}$

$\dfrac{R}{L}=[T^{-1}]$

Hence, The dimension of the $\dfrac{L}{R}$ is same of the time dimension.

Answer 2

Option 1 ( L/R ) is the correct answer.........