4.5.6 The transformer (3)
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1.
A transformer has a primary current of 2.0 A and a primary voltage of 230 V. The secondary voltage is 12.5 V. Calculate the efficiency of the transformer, assuming it operates at 100% efficiency.
Given:
- Ip = 2.0 A
- Vp = 230 V
- Vs = 12.5 V
Equation for 100% efficiency: Ip Vp = Is Vs
Calculation:
Is = (Ip Vp) / Vs
Is = (2.0 A * 230 V) / 12.5 V
Is = 460 A·V / 12.5 V
Is = 36.8 A
Efficiency = (Output Power / Input Power) * 100%
Since the transformer is assumed to be 100% efficient, Output Power = Input Power.
Therefore, Efficiency = 100%
Answer: The efficiency of the transformer is 100%.
2.
Question 1
Describe the construction of a simple transformer with a soft-iron core, as used for voltage transformations. Your answer should include details of the key components and their arrangement.
A simple transformer consists of a soft-iron core, a primary coil, and a secondary coil. The soft-iron core is typically made of laminated soft iron. Lamination reduces eddy current losses within the core. The primary coil is where the input alternating current (AC) is applied. The secondary coil is where the transformed AC voltage is induced. The primary and secondary coils are wound around the soft-iron core, typically with a certain number of turns. The arrangement is such that the primary and secondary coils are electrically isolated but magnetically linked through the core. The core provides a low-reluctance path for the magnetic flux produced by the primary coil, ensuring efficient transfer of magnetic energy to the secondary coil. The number of turns in the primary and secondary coils determines the voltage transformation ratio.
- Soft-iron core: Provides a low-reluctance path for magnetic flux and reduces eddy current losses.
- Primary coil: Receives the input AC voltage.
- Secondary coil: Where the transformed AC voltage is induced.
- Arrangement: Coils are wound around the core, magnetically linked.
3.
Question 3
A transformer has 100 turns in its primary coil and 500 turns in its secondary coil. Calculate the voltage ratio of the transformer. Explain what this voltage ratio indicates about the input and output voltages.
The voltage ratio of a transformer is directly proportional to the ratio of the number of turns in the primary and secondary coils. The formula for the voltage ratio (Vp/Vs) is:
Vp/Vs = Np/Ns
Where:
- Vp = Voltage in the primary coil
- Vs = Voltage in the secondary coil
- Np = Number of turns in the primary coil (100)
- Ns = Number of turns in the secondary coil (500)
Therefore, Vp/Vs = 100/500 = 1/5 = 0.2
This means that the secondary voltage is 1/5th of the primary voltage. Specifically, the output voltage (Vs) is 0.2 times the input voltage (Vp). Since the secondary coil has more turns than the primary coil, the transformer is a step-up transformer. This indicates that the input voltage is lower than the output voltage. The transformer increases the voltage from the primary to the secondary side.