Q4. Assertion: in a series LCR circuit at resonance, the power factor is 1. Reason: at resonance XL = XC, so φ = 0. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion (NCERT page 191).
Q5. A series circuit has R = 40 Ω and Z = 50 Ω on a 200 V rms supply. Find the current, the power factor and the average power, and check that it equals I2R.
I = 200/50 = 4.0 A, cos φ = R/Z = 0.80, and P = VI cos φ = 200 × 4.0 × 0.80 = 640 W, which equals I2R = 16 × 40 = 640 W (NCERT Eqs. [7.30(a)]–[7.30(b)], page 191).
Q6. Why is a capacitor connected in parallel with an inductive load such as a motor?
Its leading wattless current cancels the motor’s lagging wattless current, so the supply current falls towards the power component and the power factor approaches 1, cutting line losses (NCERT Example 7.7, pages 191–192).
Q7. In Example 1, what is the magnitude of the reactive (wattless) current, and how does it compare with the power component?
I = 40 A and cos φ = 0.6, so |sin φ| = 0.8: Ip = 24 A and Iq = 32 A. The wattless component is larger than the power component, because |φ| > 45° (reasoned from NCERT Example 7.8, pages 192–193).