Q4. Assertion: cutting a copper wire in half does not change its resistivity. Reason: resistivity depends on the material of a conductor but not on its dimensions. Are both true, and does the reason explain the assertion?
Both are true, and the reason explains the assertion. The resistance of each half is halved, but the resistivity is unchanged (NCERT page 84).
Q5. Wire B is made of the same material as wire A but is twice as long and has twice the diameter. Find RB/RA.
R ∝ l/A, and twice the diameter means four times the area, so RB/RA = 2/4 = 1/2 (NCERT Eq. (3.9), page 84).
Q6. A wire of resistance 10 Ω is drawn out to three times its length, its volume and resistivity staying the same. Find its new resistance.
The length is 3 times and the area 1/3, so R = 3 × 3 × 10 = 90 Ω (reasoned from NCERT Eq. (3.9), page 84).
Q7. A negligibly small current is passed through a wire 15 m long, of uniform cross-section 6.0 × 10−7 m2, and its resistance is 5.0 Ω. Find the resistivity of the material (NCERT Exercise 3.4).
ρ = RA/l = 5.0 × 6.0 × 10−7/15 = 2.0 × 10−7 Ω m (NCERT Eq. (3.9), page 84). The small current keeps the wire from heating, so this is the resistivity at the temperature of the experiment.