Question

A transformer consists of 500 turns in the primary coil and 10 turns in a secondary coil with the load of $10\Omega$. Find out the current in the primary coil when the voltage across the secondary coil is $50\;V$

& A.5A \\\ & B.0.1A \\\ & C.10A \\\ & D.2A \\\ \end{aligned}$$

Answer 1

A transformer is a device, which can step-up or step-down the given AC. This depends on the number of windings in the coil. It follows a simple ratio. Using this ratio; we can find the current in the second coil.
Formula: $\dfrac{V_{P}}{V_{S}}=\dfrac{N_{P}}{N_{S}}=\dfrac{I_{S}}{I_{P}}$

Complete answer:
Transformer is an electrical device, which can vary the current, using the principle of mutual induction. Here two coils are coupled, namely the primary and the secondary coil. The primary coil creates a varying magnetic flux, which in turn induces an EMF on the secondary coil.
The primary and the secondary coil are wound up on the core, to avoid leaking of magnetic flux .The core of the transform is decided on the basis of the magnetic permeability of the material and its economic availability.
From transformer equation, we know that,
$\dfrac{V_{P}}{V_{S}}=\dfrac{N_{P}}{N_{S}}=\dfrac{I_{S}}{I_{P}}$
Where, $V$ is the voltage, $I$ is the current in the $P$ primary and $S$ secondary coil.
Given that,$V_{S}=50$,$N_{P}=500$ and $N_{S}=10$, and substituting, we get,
$\dfrac{V_{P}}{50}=\dfrac{500}{10}$
$\implies V_{P}=2500V$
Then, the $I_{S} =\dfrac{V_{S}}{R}$
Given that $R=10\omega$
$\implies I_{S}=\dfrac{50}{10}=5A$
Since the $R$ is constant, we can say that, $\dfrac{I_{P}}{I_{S}}=\dfrac{V_{S}}{V_{P}}$
$\implies \dfrac{I_{P}}{5}=\dfrac{50}{2500}$
$\therefore I_{P}=0.1A$

Hence the answer is option $B.0.1A$ .

Additional information:
We know that the transformers carry AC current and follow Faraday's law of induction .Here the emf produced in the given circuit is equal to the negative of the change in magnetic flux in 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.

Note:
If the number of windings in the primary coil is greater as compared to that of the windings in the secondary coil, it is called a step-down transformer. Similarly, if the windings in the secondary coil are greater than that of the windings in the primary coil, it is called a step-up transformer.