Question

Suppose we have a 100 V A.C. supply, and we connect a 1 ohm resistor with it. Now the current through the resistor will be 100 A. Now we connect a 1:2 step up transformer with the A.C supply, and then connect the 1 ohm resistor with the secondary. Now, voltage across the secondary will be 200 V. And assuming that primary and secondary coils have no resistance, the current through the resistor will be 200 A. And the current through the primary will be 400 A. So, current has increased from 100 A to 200 A. But, step up transformers are used to reduce current to decrease I²R loss through transmission lines. How is it?

Answer 1

A step-up transformer increases voltage and decreases current in the primary coil according to the transformer equation, to maintain power conservation. This reduces power losses during transmission over long distances. The described scenario with currents doubling does not hold true and contradicts the conservation of power and the concept of transformers.

Step-by-step explanation:

When a 1 ohm resistor is connected to a 100 V A.C. supply, the resulting current is 100 A. If this supply is then connected to a 1:2 step-up transformer, the voltage on the secondary side becomes 200 V. In this scenario, if the resistor is connected to the secondary, the current through the resistor will be 200 A. However, there seems to be a misconception in the student's question regarding the relationship between the currents in the primary and secondary coils.

According to the transformer equation, the ratio of the secondary to primary voltages in a transformer equals the ratio of the number of turns in their windings. Additionally, a step-up transformer does not increase the current in the way described; rather, it decreases current in the primary coil. The conservation of power principle (P=IV) dictates that the power output (product of current and voltage) of the transformer is nearly equal to the power input, assuming ideal conditions with negligible resistance and high efficiency, often exceeding 99%.

This means that in a step-up transformer, although voltage increases, the current diminishes in the primary coil relative to the secondary. Specifically, for a step-up transformer with a transformation ratio of 2:1, if the secondary current is 200 A, the primary current should be 100 A because the voltage in the primary is half that of the secondary. Hence, the total power (P) remains approximately the same for both the primary and the secondary, following the equation Pp=IpVp=IsVs=Ps. So when transmitting electrical power over long distances, step-up transformers are used to increase the voltage and decrease the current in the primary, which consequently reduces I²R losses in the transmission lines.