Instructions: Read the given information carefully and answer the questions that follow:
1) The resistivity of copper is less than that of aluminum which, in turn is less than that of constantan.
2) There are nine wires, labeled as A, B, C, D, E, F, G, H, I, that have been designed as per the tabular details given below:
WIRE LENGTH DIAMETER MATERIAL RESISTANCE
2) B 2l d Constantan R2
3) C 3l d Constantan R3
4) D l d Copper R4
5) E l 2d Copper R5
6) F l 3d Copper R6
7) G l d/2 Copper R7
8) H l d/2 Constantan R8
9) I l d/2 Aluminum R9
Answer the following questions:
1. Arrange the three values R1, R2, R3 in increasing order.
2. Arrange the three valuesR7, R8, R9 in decreasing order.
3. Which of the two has a lower value
a) R4 and R6
b) R1 and R8
4. Will the graph between R1, R2, R3 ( on the y-axis) and their corresponding length values ( on the x-axis ) be a straight line?
5. What is the likely value of the ratio R4/R6?
Due to paucity of time it would not be possible for us to solve all your queries. We are providing solution to one of your queries. Try solving the rest of the questions yourself and if you face any difficulty then do get back to us.
we know that
R = ρL/A
so,
R ~ L
R ~ ρ
and
R ~ 1/A
....
now,
in the case of constantan of different length L, 2L and 3L
as R ~ L
thus,
R 1 < R 2 < R 3
and resistivities
ρconstantan > ρaluminium > ρcopper
so,
now, for same length as area of cross section
Rconstantan > Raluminium > Rcopper
so,
R 6 > R 5 > R 4
and
in case when both length and area are same
and as materials are different resistivities will we considered
so, as
ρconstantan > ρaluminium > ρcopper
so,
R 8 > R 9 > R 7