Q4. Assertion: adding a resistor in parallel to a circuit lowers its total resistance. Reason: the extra branch adds a term 1/R to 1/Rp, so 1/Rp grows. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion: a larger 1/Rp means a smaller Rp.
Q5. A 2 Ω resistor is in series with a parallel pair of 3 Ω and 6 Ω, across 12 V. Find the total current and the current in the 3 Ω resistor.
The pair gives 3 × 6/9 = 2 Ω, so the total is 4 Ω and I = 12/4 = 3 A. The pair has 3 × 2 = 6 V across it, so the 3 Ω resistor carries 6/3 = 2 A.
Q6. A wire of resistance 12 Ω is cut into three equal pieces, which are joined in parallel. Find the resulting resistance.
Each piece has 4 Ω (R ∝ l, NCERT Eq. (3.5), page 84); three in parallel give 4/3 ≈ 1.3 Ω.