Write dimensions of the given electrical quantities

• Resistance $R$: $[R] = \frac{[V]}{[I]} = M L^2 T^{-3} I^{-2}$

• Capacitance $C$: $C = \frac{Q}{V}$ Since $[Q] = IT$, $[C] = \frac{IT}{M L^2 T^{-3} I^{-1}} = M^{-1}L^{-2}T^4 I^2$

• Inductance $L$: From $V = L\,\dfrac{dI}{dt}$, $[L] = \frac{[V]\,[T]}{[I]} = M L^2 T^{-2} I^{-2}$

Check each option

Option A: $RC$

$[RC] = [R][C]$ $= \left(M L^2 T^{-3} I^{-2}\right)\left(M^{-1}L^{-2}T^4 I^2\right) = T$ So, $RC$ has the dimension of time.

Option B: $\dfrac{L}{R}$

$\left[\frac{L}{R}\right] = \frac{M L^2 T^{-2} I^{-2}}{M L^2 T^{-3} I^{-2}} = T$ So, $\dfrac{L}{R}$ has the dimension of time.

Option C: $\sqrt{LC}$

$[LC] = \left(M L^2 T^{-2} I^{-2}\right)\left(M^{-1}L^{-2}T^4 I^2\right)=T^2$ Therefore, $[\sqrt{LC}] = T$ So, $\sqrt{LC}$ also has the dimension of time.

Option D: $\dfrac{L}{C}$

$\left[\frac{L}{C}\right] = \frac{M L^2 T^{-2} I^{-2}}{M^{-1}L^{-2}T^4 I^2} = M^2 L^4 T^{-6} I^{-4}$ This is not the dimension of time.

Conclusion

The quantity that does not have the dimension of time is: $\boxed{\frac{L}{C}}$

Comparison with stored answer

Stored correct answer: $D$

Our derived answer is also $D$, so they agree.