Question

The dimensional formula of $\frac{L}{R}$ is the same as that of (where $L$ is inductance and $R$ is resistance)

• A. ${\left(frequency\right)}^2$
• B. time period
• C. frequency
• D. ${\left(timeperiod\right)}^2$

Answer 1

The correct option is B

time period

Step 1: Given

Inductance is $L$

Resistance is $R$

Step 2: Formula Used

Inductance is given as,

$L=\frac{V}{{\displaystyle \frac{{\displaystyle di}}{{\displaystyle dt}}}}$,

Where $V$ is potential difference and $\frac{di}{dt}$ is rate of change of current.

By ohm's law, $V=iR$.

Step 3: Solution

Finding the expression for $\frac{L}{R}$ using the above formulas,

$$\begin{gathered} L=\frac{V}{{\displaystyle \frac{{\displaystyle di}}{{\displaystyle dt}}}} \\ \Rightarrow L=\frac{iR}{{\displaystyle \frac{{\displaystyle di}}{{\displaystyle dt}}}}\left[\because V=iR\right] \\ \Rightarrow \frac{L}{R}=\frac{i}{{\displaystyle \frac{di}{dt}}} \end{gathered}$$

As the dimensional formula of both $i$ and $di$ are the same, they both cancel out. Thus, the dimensional formula of $\frac{L}{R}$ is the same as that of $dt$.

Thus, the dimensional formula of $\frac{L}{R}$ is,= $M^0{L}^0{T}^1$

Out of all the given options, the dimensional formula of time is = $M^0{L}^0{T}^1$.

Hence, the correct answer is option (B).