Question

On which principle does the transformer work? What are step-up and step-down transformers? Mention two main losses occurring in transformers. In an ideal transformer, the ratio of turns in primary and secondary coils is 10 : 1. Supply in primary is of 220 V and secondary is connected with a resistance of 220 \(\Omega\). Find the value of current flowing in the primary.

Hint:

In an ideal transformer, the power in the primary coil equals the power in the secondary coil. Therefore, the relationship between voltage and current is given by \(V_p I_p = V_s I_s\), where the voltage ratio is equal to the turns ratio.

Answer 1

A transformer works on the principle of electromagnetic induction and Faraday's law of induction. The voltage induced in the secondary coil is proportional to the ratio of the number of turns in the secondary coil to the number of turns in the primary coil. This relationship is given by the equation: \[ \frac{V_s}{V_p} = \frac{N_s}{N_p} \] Where \(V_s\) and \(V_p\) are the voltages in the secondary and primary coils, and \(N_s\) and \(N_p\) are the number of turns in the secondary and primary coils.
In a step-up transformer, the number of turns in the secondary coil is greater than the primary coil, which increases the voltage. In a step-down transformer, the number of turns in the secondary coil is less than the primary coil, which decreases the voltage.
Given that \(V_p = 220~\text{V}\), the ratio of turns is \(N_s / N_p = 10 / 1\), and the resistance in the secondary coil is \(R_s = 220~\Omega\), we can calculate the current flowing in the secondary coil using Ohm's law: \[ I_s = \frac{V_s}{R_s} \] Since the transformer is ideal, the voltage ratio is equal to the turns ratio: \[ V_s = \frac{N_s}{N_p} . V_p = 10 \times 220 = 2200~\text{V} \] Now, calculate the current in the secondary: \[ I_s = \frac{2200}{220} = 10~\text{A} \] By conservation of energy and assuming an ideal transformer, the current in the primary coil is related to the current in the secondary by the inverse of the turns ratio: \[ I_p = \frac{I_s}{\frac{N_s}{N_p}} = \frac{10}{10} = 1~\text{A} \]