Question

If $C,R,L$ and $I$ denote capacitance, resistance, inductance and electric current respectively, then the quantities having the same dimensions of time are
a) $CR$
b) $L/R$
c) $\sqrt{LC}$
d) ${LI}^2$

• A. a and b only
• B. a and c only
• C. a and d only
• D. a, b and c only

Answer 1

The correct option is D a, b and c only

$C=M^{-1}{L}^{-2}{I}^2{T}^4$

$R=M{L}^2{I}^{-2}{T}^{-3}$

$L=M{L}^2{I}^{-2}{T}^{-2}$
$I=I^1$
$CR=T$
$\frac{L}{R}=T$
$\sqrt{LC}=T$
$L{I}^2=M{L}^2{T}^{-2}$
Hence a, b, c have some dimension of time t.