A step-down transformer has a power output of 50 W and efficiency of 80%. if the mains supply voltage is 200 v, calculate the primary current of the transformer.
A
0.31 A
B
3.20 A
C
3.40 A
D
5.00 A
Verified Correct Answer: A.
Physical Principles & Numerical Solution
To find the primary current of the step-down transformer, we follow these steps:
1. Calculate the Power Input:
The efficiency (\( \eta \)) of the transformer is given by:
\(\eta = \frac{\text{Power Output}}{\text{Power Input}} \times 100\)
Rearranging gives:
\(\text{Power Input} = \frac{\text{Power Output}}{\eta}\)
Given:
- Power Output = 50 W
- Efficiency = 80\% = 0.80
Thus,
\(\text{Power Input} = \frac{50 \, \text{W}}{0.80} = 62.5 \, \text{W}\)
2. Calculate the Primary Current:
The power input can also be expressed in terms of voltage and current:
\(\text{Power Input} = V_p \times I_p\)
Where:
- \( V_p \) = primary voltage (given as 200 V)
- \( I_p \) = primary current (what we want to find)
Rearranging gives:
\( I_p = \frac{\text{Power Input}}{V_p}\)
Now substituting the values:
\(I_p = \frac{62.5 \, \text{W}}{200 \, \text{V}} = 0.3125 \, \text{A}\)
Thus, the primary current of the transformer is: 0.3125A
Source: WAEC / JAMB / NECO Classroom Archive (Record #14078)