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A transformer is a device that takes an input voltage and produces an output voltage that can be either larger or smaller than the input voltage, depending on the transformer design. Although the voltage is changed by the transformer, energy is not, so the input power equals the output power. A particular transformer produces an output voltage that is 300 percent of the input voltage. What is the ratio of the output current to the input current?
  • a)
    1:03
  • b)
    3:01
  • c)
    0.25
  • d)
    300:01:00
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A transformer is a device that takes an input voltage and produces an ...
We are told that transformers conserve energy so that the output power equals the input power. Thus Pout = Pin, or IoutVout = IinVin. There is therefore an inverse proportionality between current and voltage. If the output voltage is 300% of the input voltage (3 times its amount), then the output current must be 1/3 of the input voltage. This can be represented as a 1:3 ratio.
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Most Upvoted Answer
A transformer is a device that takes an input voltage and produces an ...
Understanding Transformer Basics
Transformers operate on the principle of electromagnetic induction, which allows them to change voltage levels while conserving power. The relationship between input and output voltages and currents is defined by the following key points:
Power Conservation
- The power input to a transformer (Vin * Iin) equals the power output (Vout * Iout).
- This means: Vin * Iin = Vout * Iout.
Output Voltage Calculation
- In this case, the output voltage (Vout) is 300% of the input voltage (Vin).
- Therefore, Vout = 3 * Vin.
Finding the Current Ratio
- Using the power conservation equation:
Vin * Iin = Vout * Iout
=> Vin * Iin = (3 * Vin) * Iout
- Simplifying gives:
Iin = 3 * Iout.
Current Ratio
- Rearranging the equation yields:
Iout = Iin / 3.
- This indicates the output current (Iout) is one-third of the input current (Iin).
Final Ratio
- The ratio of output current to input current is:
Iout : Iin = 1 : 3.
Thus, the correct answer is option 'A' (1:3). This demonstrates that as the voltage increases, the current decreases proportionally to maintain power balance in the transformer.
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