Q4. Assertion: joining identical cells in parallel does not increase the emf. Reason: in parallel the internal resistance falls to r/n, but εeq/req = nε/r gives εeq = ε. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion (NCERT Eqs. (3.58)–(3.59), page 97).
Q5. n identical cells, each of emf ε and internal resistance r, are joined in series across a resistance R. Find the current, and show when it is close to that from a single cell.
I = nε/(R + nr) (NCERT Eqs. (3.40), (3.45)–(3.46)), against ε/(R + r) from one cell. If R ≪ r, both are close to ε/r, so adding cells in series gains almost nothing. If R ≫ nr, I ≈ nε/R, about n times the current from one cell.
Q6. Two cells, 2.0 V with 0.10 Ω and 1.5 V with 0.30 Ω, are joined in parallel, positive to positive. Find the equivalent emf and internal resistance.
1/req = 10 + 3.33 = 13.33, so req = 0.075 Ω. εeq/req = 20 + 5 = 25, so εeq = 25 × 0.075 ≈ 1.88 V (NCERT Eqs. (3.56)–(3.57), page 97).