Math Problem Statement
Solution
The question asks to determine the secondary current and the type of transformer. Let's solve it step by step:
Given Data:
- Primary voltage () = 220 V
- Secondary voltage () = 50 V
- Primary current () = 2 A
- Efficiency () = 75% = 0.75
Formula for efficiency:
where:
- = power in the secondary circuit =
- = power in the primary circuit =
Rewriting the efficiency formula to calculate :
Substituting the values:
Conclusion for the type of transformer:
The primary voltage () is greater than the secondary voltage (). Therefore, this is a step-down transformer.
Final Answer:
- Secondary current () = 6.6 A
- Type of transformer = Step-down transformer
Would you like further explanation or have additional questions?
5 Related Questions:
- How is transformer efficiency calculated for different load conditions?
- What is the difference between a step-up and a step-down transformer?
- How do core losses affect transformer efficiency?
- Can the power output of a transformer exceed its input? Why or why not?
- What are the practical uses of step-down transformers in daily life?
Tip: Always double-check the efficiency values in transformer problems, as it directly affects the secondary current calculation.
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Math Problem Analysis
Mathematical Concepts
Transformer Efficiency
Power Calculations
Current and Voltage Relationships
Formulas
Efficiency (η) = P_s / P_p
P_s = V_s * I_s
P_p = V_p * I_p
I_s = (η * V_p * I_p) / V_s
Theorems
Law of Conservation of Energy in Transformers
Suitable Grade Level
Grades 9-12
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