Math Problem Statement

Sebuah transformator dengan tegangan primer 220 V, tegangan sekunder 50 V berarus primer 2 A. Jika efisiensi transformator 75%. Tentukan besar arus sekunder dan jenis transformator tersebut!

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 (VpV_p) = 220 V
  • Secondary voltage (VsV_s) = 50 V
  • Primary current (IpI_p) = 2 A
  • Efficiency (η\eta) = 75% = 0.75

Formula for efficiency:

η=PsPp\eta = \frac{P_s}{P_p} where:

  • PsP_s = power in the secondary circuit = VsIsV_s \cdot I_s
  • PpP_p = power in the primary circuit = VpIpV_p \cdot I_p

Rewriting the efficiency formula to calculate IsI_s: Is=ηVpIpVsI_s = \frac{\eta \cdot V_p \cdot I_p}{V_s}

Substituting the values:

Is=0.75220250I_s = \frac{0.75 \cdot 220 \cdot 2}{50} Is=33050=6.6AI_s = \frac{330}{50} = 6.6 \, \text{A}

Conclusion for the type of transformer:

The primary voltage (VpV_p) is greater than the secondary voltage (VsV_s). Therefore, this is a step-down transformer.

Final Answer:

  • Secondary current (IsI_s) = 6.6 A
  • Type of transformer = Step-down transformer

Would you like further explanation or have additional questions?


5 Related Questions:

  1. How is transformer efficiency calculated for different load conditions?
  2. What is the difference between a step-up and a step-down transformer?
  3. How do core losses affect transformer efficiency?
  4. Can the power output of a transformer exceed its input? Why or why not?
  5. 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