Question

A stepdown transformer is 75% efficient and reduces the voltage of a transmission line from 2200 V to 220 V. If the power drawn by it is 1000 W, the current obtained is
1. 34 A
2. 3.4 A
3. 4.65 A
4. 46.5 A

Answer 1

Correct Answer - Option 2 : 3.4 A

The correct answer is option 2) i.e. 3.4 A

CONCEPT:

• Step down transformer: A step-down transformer is used to convert high voltage at the primary side to low voltage at the secondary side.​

• The efficiency of the transformer (η): It is the ratio of output power to the input power.

​\(η = \frac{P_{output}}{P_{input}}\)

• Power: The rate of work done by an electric current is called power. The SI unit of power is the watt (W).

Power, P = VI 

Where V is the potential difference, and I is the current flowing.

CALCULATION:

Given that:

Input Voltage, V_i = 2200 V

Output Volatge, V_o = 220 V

Pinput = 1000 W

Efficiency (η) = 75% = 75/100 = 0.75

\(η = \frac{P_{output}}{P_{input}} \Rightarrow 0.75 = \frac{P_{output}}{1000}\)

Poutput = 750 W

P = VI

 \(\Rightarrow I = P/V\)

Output current, Ioutput = \(\frac {P_{output}}{V_o} = \frac{750}{220} =3.4 \: A\)