Solved Examples: Ideal vs Real Transformer Power Calculations

📚 Quick Study Guide

• ⚡ Ideal Transformer: Assumes no power losses. Input power ($P_{in}$) equals output power ($P_{out}$).
• 🔢 Ideal Transformer Equations:
  • $P_{in} = V_p I_p$ (Primary Voltage x Primary Current)
  • $P_{out} = V_s I_s$ (Secondary Voltage x Secondary Current)
  • $V_p I_p = V_s I_s$ (Ideal Transformer Power Conservation)
• 🔥 Real Transformer: Experiences power losses due to factors like core losses (hysteresis and eddy currents) and copper losses (resistance in windings).
• 📊 Real Transformer Equations:
  • $P_{in} = V_p I_p \cos(\theta_p)$
  • $P_{out} = V_s I_s \cos(\theta_s)$
  • Efficiency $(\eta) = \frac{P_{out}}{P_{in}} \times 100\%$
• 🔍 Key Losses in Real Transformers:
  • Core Losses: Hysteresis and eddy current losses in the core.
  • Copper Losses: $I^2R$ losses in the primary and secondary windings.
• 💡 Power Factor: The cosine of the angle between voltage and current ($\cos(\theta)$). Ideal transformers often assume a power factor of 1, but real transformers have power factors less than 1.

Practice Quiz

1. Question 1: An ideal transformer has a primary voltage of 240V and a primary current of 2A. If the secondary voltage is 120V, what is the secondary current?
1. A. 1A
2. B. 2A
3. C. 3A
4. D. 4A
2. Question 2: A real transformer has an input power of 1000W and an output power of 950W. What is the efficiency of the transformer?
1. A. 90%
2. B. 95%
3. C. 100%
4. D. 105%
3. Question 3: Which of the following is NOT a source of power loss in a real transformer?
1. A. Core Losses
2. B. Copper Losses
3. C. Hysteresis Losses
4. D. Ideal Windings
4. Question 4: In an ideal transformer, if the primary voltage is halved and the number of turns in the primary winding remains constant, what happens to the secondary voltage?
1. A. Doubles
2. B. Halves
3. C. Remains the same
4. D. Becomes zero
5. Question 5: A transformer has a primary voltage of 200V and a primary current of 5A. The secondary voltage is 100V and the secondary current is 9A. What is the efficiency of this transformer?
1. A. 80%
2. B. 90%
3. C. 95%
4. D. 100%
6. Question 6: What causes core losses in a real transformer?
1. A. Resistance in the windings
2. B. Hysteresis and eddy currents
3. C. High voltage
4. D. Low current
7. Question 7: A transformer has a power factor of 0.8. If the apparent power is 1000 VA, what is the real power?
1. A. 600 W
2. B. 700 W
3. C. 800 W
4. D. 900 W