Question

A transformer having efficiency \(90\%\) is working on \(200\) V and \(3\) KW power supply. If the current in the secondary coil is \(6\)A, the voltage across the secondary coil and the current in the primary coil, respectively, are

• A. \(300\) V, \(15\) A
• B. \(450\) V, \(15\) A
• C. \(450\) V, \(13.5\) A
• D. \(600\) V, \(15\) A

Hint:

Find the primary current from input power and primary voltage, then find the secondary voltage from output power and secondary current.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Efficiency of a transformer is the ratio of output power to input power.
Input power and primary voltage give the primary current, and output power with secondary current gives the secondary voltage.

Step 2: Primary Current
Input power \(P_{in} = 3000\) W and primary voltage \(V_p = 200\) V.
\(I_p = \dfrac{P_{in}}{V_p} = \dfrac{3000}{200} = 15\) A

Step 3: Output Power
\(P_{out} = \eta \times P_{in} = 0.90 \times 3000 = 2700\) W

Step 4: Secondary Voltage
\(V_s = \dfrac{P_{out}}{I_s} = \dfrac{2700}{6} = 450\) V

Step 5: Compare the options
The secondary voltage is \(450\) V and the primary current is \(15\) A, which matches option (B).

Final Answer:
The secondary voltage is 450 V and the primary current is 15 A. \[ \boxed{\text{(B) }\text{450 V, 15 A}} \]