Question

If $L, R, C$ denote inductance, resistance and capacitance, respectively. Then dimensions of $\frac{L}{R^{2}C}$ are

• A. $\left[M^{0}L^{0}T\right]$
• B. $\left[MLT^{-1}\right]$
• C. $\left[A^{-1}M^{0}L^{0}T^{-1}\right]$
• D. $\left[M^{0}L^{0}T^{0}\right]$

Answer 1

Answer: (D)

$\frac{L}{R}=$ time constant of $L-R$ circuit $=\left[M^{0}L^{0}T\right]$
$RC =$ time constant of $R-C$ circuit $=\left[M^{0}L^{0}T\right]$
$\therefore $ The dimensions of
$\frac{L^{2}}{R^{2}C}=\left(\frac{L}{R}\right)\times\frac{1}{RC}$
$=\frac{\left[M^{0}L^{0}T\right]}{M^{0}L^{0}T}=\left[M^{0}L^{0}T^{0}\right]$