a power transmission line feeds input power at 2400 V to a step down ideal transformer having 4000 turns in its primary. What should be number of turns in its secondary to get power output at 240V

To determine the number of turns in the secondary winding of the transformer, we can use the transformer turns ratio formula. This formula relates the primary and secondary voltages to the number of turns in the primary and secondary coils. The relationship is given by:

Transformer Turns Ratio

The formula for the transformer turns ratio is:

Vp / Vs = Np / Ns

Where:

• Vp = Primary voltage
• Vs = Secondary voltage
• Np = Number of turns in the primary winding
• Ns = Number of turns in the secondary winding

Given Values

From your question, we have:

• Vp = 2400 V
• Vs = 240 V
• Np = 4000 turns

Calculating the Number of Turns in the Secondary

We can rearrange the formula to solve for the number of turns in the secondary winding (Ns):

Ns = (Vs / Vp) * Np

Now, substituting the known values into the equation:

Ns = (240 V / 2400 V) * 4000 turns

Calculating the fraction:

Ns = (1 / 10) * 4000 turns

Ns = 400 turns

Final Result

Therefore, to achieve an output voltage of 240 V from a primary voltage of 2400 V with a primary winding of 4000 turns, the secondary winding should have 400 turns.

Understanding the Concept

This calculation illustrates how transformers work based on the principle of electromagnetic induction. The voltage is stepped down by reducing the number of turns in the secondary coil relative to the primary coil. This is crucial in power distribution systems, where high voltages are used for efficient transmission over long distances, and lower voltages are needed for safe usage in homes and businesses.