Q4. Assertion: a capacitor lets high-frequency ac through more easily than low-frequency ac. Reason: its reactance XC = 1/(2πνC) falls as the frequency rises. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion (NCERT page 185).
Q5. A capacitor draws 0.50 A rms from a 100 V, 50 Hz supply. Find its capacitance.
XC = 100/0.50 = 200 Ω, so C = 1/(2π × 50 × 200) ≈ 1.6 × 10−5 F, about 16 µF (NCERT Eqs. (7.17)–(7.18), page 184).
Q6. An inductor and a capacitor have equal reactances of 50 Ω at 1.0 kHz. What are their reactances at 2.0 kHz?
XL ∝ ν doubles to 100 Ω, and XC ∝ 1/ν halves to 25 Ω (NCERT pages 182 and 185).
Q7. How does the energy stored in a capacitor change during one quarter cycle when the voltage rises from zero to its peak, and what happens in the next quarter?
The stored energy ½Cv2 rises from zero to its largest value, with energy flowing in from the source; in the next quarter, as v falls to zero, the capacitor returns that energy, so the net energy over a cycle is zero (reasoned from NCERT Eq. (7.19), page 185).