Question

The output of a step down transformer is measured to be 48V when connected to a 12 W bulb.The value of peak current is
A. $\sqrt{2}A$
B. $\dfrac{1}{2\sqrt{2}}A$
C. $\dfrac{1}{4\sqrt{2}}A$
D. $\dfrac{1}{\sqrt{2}}A$

Answer 1

To solve this question we need the knowledge about a circuit with alternating current. Use the relation between power, rms values of voltage and current in an AC circuit and find the rms value of the current. Then calculate the peak current.

Formula used:
$P={{V}_{rms}}{{I}_{rms}}$
where P is power and ${{V}_{rms}}$, ${{I}_{rms}}$ are the rms (root mean square) values of voltage and current.
${{I}_{0}}=\dfrac{{{I}_{rms}}}{\sqrt{2}}$
where ${{I}_{0}}$ is the peak value of current.

Complete step by step answer:
In an AC circuit, the power of the circuit is given as $P={{V}_{rms}}{{I}_{rms}}$ ….. (i).
It is given that the transformer is connected to a 12 W bulb. This means that the transformer circuit needs to generate a power of $P=12W$. And it is given that ${{V}_{rms}}=48V$.
Substitute the values in (i).
$12=(48){{I}_{rms}}$
$\Rightarrow {{I}_{rms}}=\dfrac{12}{48}=\dfrac{1}{4}A$.
Therefore value of peak current is,
${{I}_{0}}=\dfrac{{{I}_{rms}}}{\sqrt{2}}\\\ \therefore{{I}_{0}}=\dfrac{1}{4\sqrt{2}}A$

Hence, option (C) is correct.

Additional Information:
Transformer is an electronic device used to change the peak value of the voltage or the peak value of the current of an input circuit. A transformer works on the principle of electromagnetic induction. There are two types of transformers – step up transformer and step down transformer.

A step up transformer is a transformer in which the voltage of the input current is increased. This means that the peak value of the voltage of the output circuit is more than that of the input circuit. A step down transformer is a transformer in which the voltage of the input current is reduced. This means that the peak value of the voltage of the output circuit is less than that of the input circuit.

Note: The phenomenon of electromagnetic induction is valid only when there is a change current or a changing magnetic field. Therefore, voltage or energy sources in a transformer must AC sources and not DC sources. This is because a DC source produces constant potential difference whereas an AC source produces varying potential difference.