Question

A transformer works on the principle of:
A.) Self induction
B.) Electrical inertia
C.) Mutual induction
D.) Magnetic effect of the electric current

Answer 1

Hint: A transformer consists of two coils wound on a single core. One of the coils is given an input voltage. This produces a current in the coil and hence a magnetic flux is produced in the core. This magnetic flux links to the second coil and hence produces a voltage in the second coil through Faraday’s law of electromagnetic induction.
Formula used:
Faraday’s law of electromagnetic induction states that an emf is generated in a coil kept in changing magnetic flux. Mathematically, the expression is given by

$E=-\dfrac{d{{\phi }_{B}}}{dt}$

where E is the emf produced, $\dfrac{d{{\phi }_{B}}}{dt}$ is the instantaneous rate of change of magnetic flux $\left( {{\phi }_{B}} \right)$ linking through the coil with time $\left( t \right)$. The negative sign is indicative of the direction of the voltage and emphasizes that the emf tends to oppose the change in magnetic flux.

Complete step by step answer:

A transformer is a device that is used to increase or decrease an input voltage. It consists of two coils that are wound on the same laminated core. An input voltage is applied to one of the coils known as the primary coil. This produces a current in the second coil known as the secondary coil and a resulting magnetic flux is produced throughout the core.
This magnetic flux links to the secondary coil and produces a subsequent voltage in the secondary coil due to Faraday’s law of electromagnetic induction.

Faraday’s law of electromagnetic induction states that an emf is generated in a coil kept in changing magnetic flux. Mathematically, the expression is given by

$E=-\dfrac{d{{\phi }_{B}}}{dt}$

where E is the emf produced, $\dfrac{d{{\phi }_{B}}}{dt}$ is the instantaneous rate of change of magnetic flux $\left( {{\phi }_{B}} \right)$ linking through the coil with time $\left( t \right)$. The negative sign is indicative of the direction of the voltage and emphasizes that the emf tends to oppose the change in magnetic flux.

Mutual induction is the phenomenon in which a current carrying coil produces a magnetic flux which links to another coil and this induces a resultant emf in the second coil. In self induction, the magnetic flux produced by a current carrying coil links with itself and produces a voltage which tries to oppose the current and change in magnetic flux.

Now, since the transformer works because flux produced by the primary coil links to the secondary coil and produces a voltage in it, it works on the principle of mutual induction.

Hence, the correct answer is C) Mutual induction.

Note: Students might get confused thinking that since the primary coil produces a magnetic flux, hence the transformer works on the principle of the magnetic effect of electric current and hence, may be tempted to mark option D) as the correct answer.
However, that is completely wrong since the purpose of a transformer is not to produce a magnetic flux, but to alter an input voltage. Hence, the main principle which is at work here is the one that is explained above, that is the principle of mutual induction.