Question

For a circuit, L, C and R represent the inductance, capacitance and resistance. Then, the dimensional formula for $C^{2}LR$ is

• A. $\left[MLT\right]$
• B. $\left[M^0{L}^{0}T{I}^0\right]$
• C. $\left[M^2{L}^2{T}^0{I}^0\right]$
• D. $\left[M^0{L}^0{T}^3{I}^0\right]$

Answer 1

Answer: (D)

$\left[M^0{L}^0{T}^3{I}^0\right]$

The ratio of inductance L to resistance R is time constance T, hence, we have
$\left[\frac{L}{R}\right]=T$ and $\sqrt{LC}=T$
Using these two relation we have
$C^{2}LR=\left[C^2{L}^2\right]\times \left[\frac{L}{R}\right]=\left[T^4\right]\times \left[\frac{1}{T}\right]=\left[T^3\right]$