Question

Given below are two statements, Assertion $\left(A\right)$ and Reason $\left(R\right)$.

Assertion $\left(A\right)$ : The quantity $L/R$ possesses the dimension of time.

Reason $\left(R\right)$ : To reduce the rate of increase of current through a solenoid, time constant $\left(L/R\right)$ should be increased.

Based on these statements, the correct answer is -

• A. Both $A$ and $R$ are true, and $R$ is the correct explanation of $A$.
• B. Both $A$ and $R$ are true, and $R$ is NOT the correct explanation of $A$.
• C. $A$ is true, but $R$ is false.
• D. $A$ is false, but $R$ is true.

Answer 1

The correct option is B Both $A$ and $R$ are true, and $R$ is NOT the correct explanation of $A$.

We know that, induced EMF,

$e=L\frac{di}{dt}$

So,

$I=\frac{e}{R}=\frac{L}{R}\frac{di}{dt}...\left(1\right)$

Now,

$\left[I\right]=\left[\frac{L}{R}\frac{di}{dt}\right]$

$\Rightarrow \left[I\right]=\left[\frac{L}{R}\right]\left[\frac{di}{dt}\right]$

$\Rightarrow \left[\frac{L}{R}\right]=\left[dt\right]=\left[T\right](\because [I]=[di\left]\right)$

$\therefore \frac{L}{R}$ has dimension of time.

From $\left(1\right)$,

$\frac{di}{dt}=\frac{I}{L/R}$

So, $\frac{di}{dt}\downarrow$ if $L/R\uparrow$

Hence, option $\left(B\right)$ is the correct answer.