Question

Which of the following can induce the maximum induced voltage?
A. $1$ Amp dc
B. $1$ Amp $1Hz$
C. $1$ Amp $100Hz$
D. $20$ Amp dc

Answer 1

In order to solve this question, we will understand Faraday’s Second law of induction which states that induced electromotive force (EMF) or induced voltage is directly proportional to rate of change of magnetic flux. So in short if there is frequent change in flux then induced voltage is large. Also we would use the fact that frequency is inversely proportional to temperature so less the time is more the frequency or vice versa.

Complete step by step answer:
According to Faraday’s Second Law, induced Voltage depends on how fast magnetic flux is changing. Now there are two ways to increase this. Let us discuss case $1$ .We can increase magnetic flux which can be increased by increasing current and second case $2$ is to decrease time period which can be done by increasing frequency.

In here option [D] $20$ Amp dc and option [A] $1$ Amp dc has constant current so it produces a constant magnetic field which is not changing with time so magnetic flux through it is not changing hence no induced current. Also [B] $1$ Amp $1Hz$ has lesser frequency so it takes more time and that’s why change in magnetic flux is small hence induced voltage is less. So checking each option we found that $100Hz$ frequency is maximum so the time period is less so the rate of change of magnetic flux increases. So induced voltage is maximum for [C] $1$ Amp $100Hz$

Hence, the correct option is C.

Note: It should be remembered that, induced voltage is maximum when change in magnetic flux is maximum or the time period is less, since frequency and time period are mathematically related as $f = \dfrac{1}{T}$ and the relation between magnitude of voltage and magnetic flux is written as $\left| e \right| = \dfrac{{d{\varphi _B}}}{{dt}}$ where ${\varphi _B}$ is the magnetic flux which is the product of magnetic field and the perpendicular area crossing the magnetic field lines.