Q4. Assertion: when an ideal battery of constant voltage V charges an initially uncharged capacitor through a dissipative circuit to final charge Q, the battery does work QV, but the capacitor stores only ½QV. Reason: the other half is lost as heat (and radiation) while the charging current flows. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion. The battery keeps its potential difference V while it drives charge Q from one plate to the other, so it does work QV (reasoned from potential difference as work per unit charge, NCERT Section 2.11, page 67). The capacitor stores only ½QV (NCERT Eq. (2.69), page 74). The other ½QV is lost as heat and electromagnetic radiation while the current flows, as in NCERT Example 2.10 (page 76).
Q5. A charged capacitor is disconnected from its battery, and a dielectric with K = 4 is slid in to fill the gap. What happens to its stored energy?
Q stays the same and C becomes 4C, so U = Q/2C falls to a quarter of its value (reasoned from NCERT Eqs. (2.54) and (2.69), pages 70 and 74).
Q6. A 2.0 µF capacitor charged to 100 V is disconnected from its supply and joined, positive plate to positive plate, to an uncharged 3.0 µF capacitor. Find the common potential difference and the energy lost.
The charge 2.0 × 10−6 × 100 = 2.0 × 10−4 C is shared over 5.0 µF, so V = 40 V. The energy falls from ½ × 2.0 × 10−6 × 1002 = 1.0 × 10−2 J to ½ × 5.0 × 10−6 × 402 = 4.0 × 10−3 J, so 6.0 × 10−3 J is lost (reasoned from NCERT Eq. (2.69) and Example 2.10, pages 74–76).