Question

If L, R, C and V respectively, represent inductance, resistance, capacitance and potential difference, then the dimensions of L/RCV are the same as those of

• A. $\frac{1}{Charge}$
• B. Charge
• C. Current
• D. $\frac{1}{Current}$

Answer 1

The correct option is D

$\frac{1}{Current}$

Fundamental Quantity: It is an independent physical quantity that is used to define other physical quantities.

Dimensional formula: It is an expression that shows the power to which a fundamental quantity is used to obtain one unit of a derived quantity.

Step 1: Given

Inductance$=L$

Resistance$=R$

Capacitance$=C$

Potential difference$=V$

Step 2: State the dimensions of the given quantities

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

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

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

$V=M{L}^2{I}^{-1}{T}^{-3}$

Step 3: Determine the dimension of the given quantity

$$\begin{gathered} \frac{L}{RCV}=\frac{M{L}^2{I}^{-2}{T}^{-2}}{\left(M{L}^2{I}^{-2}{T}^{-3}\right)\left(M^{-1}{L}^{-2}{I}^2{T}^4\right)\left(M{L}^2{I}^{-1}{T}^{-3}\right)} \\ =M^0{L}^0{I}^{-1}{T}^0 \\ =\frac{1}{Current} \end{gathered}$$

Hence, option (D) is the correct option.