Question

Induced emf in the coil depends upon
A) Conductivity of coil
B) Amount of flux
C) Rate of change of linked flux
D) Resistance of coil

Answer 1

The induced emf set up in any circuit is directly proportional to the rate of change in magnetic flux or the linked flux. This statement is made in accordance with Faraday’s laws of electromagnetic induction and Faraday's Flux rule.

Formula used:
According to Faraday’s laws of electromagnetic induction: $E = k\dfrac{{d\phi }}{{dt}}$
where, $E$ is emf and$\dfrac{{d\phi }}{{dt}}$rate of change of magnetic flux with respect to time.

Complete step by step answer:
When the magnetic flux linked with a circuit changes, emf set up in the circuit is called as induced emf. The current due to induced emf is called as induced current. The induced emf lasts as long as the change in magnetic field continues.
The magnetic flux is defined as the dot product of magnetic field $\overrightarrow B$and the area element$d\overrightarrow A$and it is denoted by $\phi$. If $\overrightarrow B$is the magnetic field through the area element$d\overrightarrow A$, then the flux through the area is given by $d\phi = \overrightarrow B d\overrightarrow A$. The unit of magnetic flux is ‘Weber’ abbreviated as ‘Wb’.
According to Faraday's laws of electromagnetic induction, the magnitude of induced emf (can also be denoted as E) is directly proportional to the rate of change in magnetic flux or the linked flux. If $d\phi$is the change in magnetic flux during time $dt$then,
$E \propto \dfrac{{d\phi }}{{dt}}$
It can be also written as
$E = k\dfrac{{d\phi }}{{dt}}$
where $k$is the constant of proportionality. In SI units, $k = - 1$.
Hence, $E = - \dfrac{{d\phi }}{{dt}}$.
It is also called Faraday's Flux rule.

So, the correct answer is “Option C”.

Note:
The negative sign indicates that the induced emf opposes the change in magnetic flux or the linked flux. In SI units, the change in the flux $d\phi$ is measured in weber, $dt$in second and $E$in volt. Hence according to this, the unit of Volt = weber/second.