Question

The quantities $RC$ and $(L/R)$ (where $R,L$ and $C$ stand for resistance, inductance and capacitance respectively) have the dimension of

• A. force
• B. linear momentum
• C. linear velocity
• D. time

Answer 1

Answer: (D)

$RC=\mathrm{ohm}\times$ farad $=\mathrm{ohm}\times \frac{\text{ coulomb }}{\text{ volt }}$
$=\frac{\text{ volt }}{\text{ ampere }}\times \frac{\text{ coulomb }}{\text{ volt }}=\frac{\text{ volt }}{\text{ ampere }}\times \frac{\text{ ampere }\times \text{ second }}{\text{ volt }}$
$=$ second $=[T]$
$\frac{L}{R}=\frac{\text{ henry }}{\text{ ohm }}=\frac{\text{ ohm }\times \text{ second }}{\text{ ohm }}=$ second $=[T]$
Both $RC$ and $\frac{L}{R}$ have the dimensions of time.