Question

A step-up transformer of turns $2:1$ has $50Hz$ AC voltage applied to primary. The frequency of AC output voltage across the secondary is:

& A.0 \\\ & B.25Hz \\\ & C.50Hz \\\ & D.100Hz \\\ \end{aligned}$$

Answer 1

A transformer is a device which transfers electrical energy. It is based on the principles of magnetic induction, where the changing magnetic flux induces the change in the currents. It has two coils which are winded on a magnetic core.

Formula used:
$V=-N\dfrac{d\phi}{dt}$

Complete answer:
We know that the transformers carry AC current and follow Faraday's law of induction, where the emf produced in a circuit is equal to the negative of the change in magnetic flux of the circuit. We also know that magnetic flux is the number of magnetic field lines passing through a given surface area.

From faraday’s law, we get $V=-N\dfrac{d\phi}{dt}$, where $V$ is the instantaneous voltage, $N$ is the number of windings on the core, $\dfrac{d\phi}{dt}$ is the change in magnetic flux $\phi$.
Clearly,$\dfrac{d\phi}{dt}$ is constant for any given transformer.

Then, we can say that, $\dfrac{V_{p}}{V_{s}}=\dfrac{N_{p}}{N_{s}}$, where $V_{p}, N_{p}$ denote the voltage and the number of windings in the primary coil and $V_{s}, N_{s}$ denote the voltage and the number of windings in the secondary coil .

Given that $\dfrac{N_{p}}{N_{s}}=\dfrac{2}{1}$ and $f=50Hz$
The number of windings doesn’t affect the frequency of the AC in the circuit. In fact the frequency of an AC is constant, in India it is $50Hz$.
Hence the frequency of the output also remains as $50Hz$.

So, the correct answer is “Option C”.

Note:
Transformers are generally of two, step-up and step-down. In step-up transformers the number of windings in the primary coil is greater than the windings in the secondary coil. In step- down transformers, the number of windings in the primary coil is lesser than the windings in the secondary coil.