Question

Draw a labeled diagram of a step-up transformer. Obtain the ratio of secondary to primary voltage in terms of the number of turns and current in the two coils.

Answer 1

Definition of a step-up transformer:

1. A transformer is an electrical device that transforms the electrical energy (in the primary coil) into magnetic energy (in the magnetic coil) and then back again into electrical energy (in the secondary coil).
2. A step-up transformer is a device that converts a low voltage high current into a high voltage low current.
3. The transformer works on the principle of faradays law which is $V=\frac{-d\varphi }{dt}$.
4. The ac current is passed through the primary coil which produces a change in the magnetic field of the magnetic core which in turn produces a current in the secondary coil.

Given below is a labelled diagram of the step-up transformer,

Calculation of the ratio of secondary to primary voltage in terms of the number of turns and current in the two coils:

Step 1: Given

Let the alternating voltage, alternating current, and the number of turns in the primary and secondary coil be $V_1,I_1,N_1$and $V_{2,}{I}_2,N_2$.

Magnetic flux in a coil is proportional to the number of turns.

Therefore $\frac{{\varphi }_{sec}}{{\varphi }_{pri}}=\frac{N_2}{N_1}$

Here,

$\varphi$ indicates flux in a coil.

Step 2: Calculation

${\varphi }_{sec}=\frac{N_2}{N_1}{\varphi }_{pri}$

$\frac{d{\varphi }_{sec}}{dt}=\frac{N_2}{N_1}\frac{d{\varphi }_{pri}}{dt}$

But according to faradays law $V=\frac{-d\varphi }{dt}$

Therefore $\frac{V_2}{V_1}=\frac{N_2}{N_1}$

Let us assume a 100 percent efficiency.

This implies input power= output power

$V_1{I}_1=V_2{I}_2$

Hence, the ratio of secondary to primary voltage will be $\frac{V_2}{V_1}=\frac{N_2}{N_1}=\frac{I_1}{I_2}$.