(i) A wire of resistivity p is stretched to double it's length, what is it's new resistivity. Give reason for your answer.
(ii) Draw a schematic diagram of a circuit consisting of a battery of three cells of 2V each, a 511 resistor, 80 resistor and 120 resistor and a plug key all connected in series.
(iii) Two wires, one of copper and other of manganese have equal lengths and equal resistances. Which is thicker ? (Given that resistivity of manganese is lower than that of copper.)
CBSE Class X Science SA 2 (3 Marks)
Answers
Explanation:
1. half of the restivity before doubling it because length of the wire is inversly proportional to resistance
2. in fig
3. manganese
Answer:
(i) When a wire is stretched to double its length, the area of the cross-section of the wire becomes halved. The resistance of a wire is directly proportional to the length and inversely proportional to the area of the cross-section.
R = (p x l)/ A
if the length is doubled, the new length is 2l
the new area becomes A/2
so new resistance is
R' = (p x 2l) / (A/2)
R' = (4 x p x l) / A
Resistance increases by four times.
(iii) As the length of both the wires is equal and the resistivity of copper wire is more, the area of the cross-section of the copper wire should be less.
R = (p x l)/A
On increasing the numerator, the denominator should be decreased to keep the same value. This is why the copper wire is thicker than the magnesium wire with the same resistance.
(ii) The schematic circuit diagram:
