Calculate current drawn by the primary of a transformer which steps down 200V to 20V to operate a device of resistance 20ohm . Assume the efficiency of transformer to be 80%.

To find the current drawn by the primary of a transformer that steps down voltage from 200V to 20V, we need to consider a few key factors, including the load resistance, the efficiency of the transformer, and the relationship between primary and secondary currents. Let's break this down step by step.

Understanding Transformer Basics

A transformer operates on the principle of electromagnetic induction and consists of primary and secondary coils. The voltage ratio between these coils is directly related to the turns ratio. For a step-down transformer, the primary voltage (Vp) is higher than the secondary voltage (Vs).

Given Values

• Primary Voltage (Vp) = 200V
• Secondary Voltage (Vs) = 20V
• Load Resistance (R) = 20 ohms
• Efficiency (η) = 80% or 0.8

Calculating Secondary Current

First, we need to calculate the current flowing through the secondary coil. Using Ohm's Law, we can find the secondary current (Is) as follows:

Ohm's Law: I = V / R

Substituting the values for the secondary side:

Is = Vs / R = 20V / 20Ω = 1A

Finding Primary Current

Next, we need to relate the primary current (Ip) to the secondary current (Is) using the efficiency of the transformer. The efficiency formula is given by:

Efficiency (η) = (Power out / Power in)

Power out (Pout) can be calculated as:

Pout = Vs * Is = 20V * 1A = 20W

Now, since the transformer is 80% efficient, we can find the input power (Pin):

Pin = Pout / η = 20W / 0.8 = 25W

Calculating Primary Current

Now that we have the input power, we can find the primary current (Ip) using the primary voltage:

Pin = Vp * Ip

Rearranging gives us:

Ip = Pin / Vp = 25W / 200V = 0.125A

Final Result

Thus, the current drawn by the primary of the transformer is 0.125A.

In summary, by understanding the relationships between voltage, current, resistance, and efficiency, we can effectively calculate the current in both the primary and secondary sides of a transformer. This process illustrates the importance of these concepts in electrical engineering and practical applications.