Question

Given below are two statements labelled as Assertion (A) and Reason (R).

Assertion (A) : The charge flown through a cross-section of wire in shape of loop of resistance $R$, when the magnetic flux changes by $\Delta \varphi$, is independent of the time in which the flux change is brought.

Reason (R) : For a magnetic flux change of $\Delta \varphi$, the charge flown through a cross-section of wire in shape of loop of resistance $R$ is, $Q=\frac{\Delta \varphi }{R}$

Select the most appropriate answer from the options given below.

​​​​​​​$[$0.77 Mark$]$

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

Answer 1

The correct option is A Both A and R are true, and R is the correct explanation of A.

EMF induced is given by,

$|E|=\frac{\Delta \varphi }{\Delta t}$

So, induced current, $i=\frac{|E|}{R}=\frac{\Delta \varphi /\Delta t}{R}=\frac{\Delta \varphi }{R\Delta t}$

Now, the amount of induced charge flowing through the cross-section of wire,

$Q=i\Delta t=\frac{\Delta \varphi }{R\Delta t}\times \Delta t=\frac{\Delta \varphi }{R}$

$\therefore$ The charge flown is independent of time in which the magnetic flux is changed.