Primary side of a transformer is connected to 230 V, 50 Hz supply. Turns ratio of primary to secondary winding is 10 : 1. Load resistance connected to secondary side is 46 \(\Omega \). The power consumed in it is :
- 12.5 W
- 10.0 W
- 11.5 W
- 12.0 W
The Correct Option is C
Approach Solution - 1
To find the power consumed by the load resistance connected to the secondary side of the transformer, we need to follow these steps:
- Calculate the voltage across the secondary winding using the turns ratio. The turns ratio of the transformer is given as 10:1, meaning the primary winding has 10 times more turns than the secondary winding.
- The voltage across the secondary (\( V_s \)) can be calculated using the formula for voltage transformation in transformers:
\( V_s = \frac{V_p}{\text{turns ratio}} \)
- where \( V_p = 230 \, \text{V} \) is the primary voltage.
\( V_s = \frac{230}{10} = 23 \, \text{V} \)
- Using Ohm's Law, calculate the current flowing through the load resistance:
\( I_s = \frac{V_s}{R} \)
- where \( R = 46 \, \Omega \).
\( I_s = \frac{23}{46} = 0.5 \, \text{A} \)
- Calculate the power consumed by the load:
\( P = I_s^2 \times R \)
\( P = (0.5)^2 \times 46 = 0.25 \times 46 = 11.5 \, \text{W} \)
Therefore, the power consumed in the load resistance is 11.5 W.
The correct answer is 11.5 W.
Approach Solution -2
Given:
\(\frac{V_1}{V_2} = \frac{N_1}{N_2} = 10 \implies V_2 = \frac{230}{10} = 23 \, \text{V}.\)
Power consumed:
\(P = \frac{V_2^2}{R} = \frac{23 \times 23}{46} = 11.5 \, \text{W}.\)
The Correct answer is: 11.5 W
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