If a transformer has a 120-turn primary and is connected to a 60-volt source, what will be the voltage across the 80-turn secondary?
A. 400 volts
B. 160 volts
C. 90 volts
D. 40 volts
The correct answer and explanation is:
The correct answer is C. 90 volts.
Explanation:
A transformer operates on the principle of electromagnetic induction and relates the voltages in the primary and secondary coils to the number of turns in each coil. The voltage across the coils is proportional to the number of turns. This is expressed by the formula: VpVs=NpNs\frac{V_p}{V_s} = \frac{N_p}{N_s}
Where:
- VpV_p = voltage in the primary coil
- VsV_s = voltage in the secondary coil
- NpN_p = number of turns in the primary coil
- NsN_s = number of turns in the secondary coil
Given data:
- Np=120N_p = 120 turns
- Vp=60V_p = 60 volts
- Ns=80N_s = 80 turns
To find the secondary voltage VsV_s, rearrange the formula: Vs=Vp×NsNpV_s = V_p \times \frac{N_s}{N_p}
Substitute the values: Vs=60×80120=60×23=40×2=80 voltsV_s = 60 \times \frac{80}{120} = 60 \times \frac{2}{3} = 40 \times 2 = 80 \text{ volts}
Recalculation for accuracy:
60×80120=60×0.6667=4060 \times \frac{80}{120} = 60 \times 0.6667 = 40 volts approximately. But the options do not have 80 volts; let’s check carefully.
Wait, my first calculation was 80 volts, but the multiplication is: 60×80120=60×0.6667=40 volts60 \times \frac{80}{120} = 60 \times 0.6667 = 40 \text{ volts}
This suggests 40 volts, which corresponds to option D.
So there is a contradiction. Let me verify.
Step 1: Calculate the ratio of turns: NsNp=80120=23≈0.6667\frac{N_s}{N_p} = \frac{80}{120} = \frac{2}{3} \approx 0.6667
Step 2: Calculate secondary voltage: Vs=Vp×NsNp=60×0.6667=40 voltsV_s = V_p \times \frac{N_s}{N_p} = 60 \times 0.6667 = 40 \text{ volts}
Therefore, the correct secondary voltage is 40 volts.
Conclusion:
The correct answer is D. 40 volts.
Detailed Explanation:
Transformers change voltage levels according to the ratio of turns in the coils. When the secondary coil has fewer turns than the primary coil, the transformer reduces the voltage; this is called a step-down transformer. If the secondary has more turns, the voltage is increased, making it a step-up transformer.
In this problem, the secondary coil has 80 turns, which is less than the 120 turns in the primary coil. This means the transformer reduces the voltage from 60 volts at the primary side to a lower voltage on the secondary side.
The proportionality between voltage and turns means that the secondary voltage is: Secondary Voltage=Primary Voltage×Secondary TurnsPrimary Turns\text{Secondary Voltage} = \text{Primary Voltage} \times \frac{\text{Secondary Turns}}{\text{Primary Turns}}
Applying the values: Vs=60×80120=60×0.6667=40 voltsV_s = 60 \times \frac{80}{120} = 60 \times 0.6667 = 40 \text{ volts}
This shows the secondary voltage is 40 volts.
Summary:
- Transformer voltage ratio equals turns ratio.
- Secondary voltage = primary voltage × (secondary turns ÷ primary turns).
- With fewer turns in the secondary, the output voltage decreases.
- Hence, the output voltage is 40 volts (option D).