resistance numericals in relation to area and length

Resistance
RESISTANCE

1.Resistance denoted by R

2.Its units are ohms

3.Definition is
obstruction to flow of charge is called resistance

4.laws of resistance
resistance is directly proportional to length of conductor
R∝L
resistance is inversely proportinal to area of the conductor
Rα1/A
RαL/A
removing proportinality constant keep a constant rho(p)
R=pl/A

5.where rho p is called as resistivity or specific resistance

6.resistance also depends on material and temperature also

7.more resistance more temperature because of more friction between electrons

8.resistivity rho p only depend on material
Not on length and area

9.resistivity
definition
Resistance of cube of one meter square area
And one meter length
When current is passing perpendicular to one of its surfaces

10.reverse of resistance is conductance and units are mho

11.reverse if resistivity is conductivity


Numericals to practice

1.find resistance of 10 m of conductor of area of cross section 2 meter square with resistivity 1.6x10power minus 10 ohm.m

2 find resistance when 2.2 m of wire of radius 1cm with p=2×10 power minus 10 ohm.m

3.find resistance if p=2.2x10 minus 12 and length 20 m with diameter 2mm

4.find resistance if p= 4.4x10 power minus 13 ohm m.of length 10 m and diameter 4mm

5.find R if p=3.14×10^minus 10 ohm.m and L= 20 m and D = 8mm

6.find R if p=2.2x10^ minus 10 ohm. M
L= 200m and D= 4mm

7.find change in resistance and resistivity if length is stretched to double its length and percentage increase in resistance

8.find change in resistance and resistivity if length is made half and area is doubled and also percentage change

9.find change in resistance and resistivity  and also percentage change in faloowing cases
A.lenth made one third and area made double
B.length made triple and radius doubled
C.lenth made one fourth and radius tripled
D.length made 10 times and diameter made double
E.lenth made two third and radius made two fifth

10..Define resistance.
On what factors resistance depends.
Find resistance when 2.2x10^-10 ohm.m resistivity of wire of length 2000 cm and diameter 4mm.

11what happens to resistance and resistivity if a wire of length l and radius r is stretched to double of its length.

12.What will be the resistivity of a metal wire of 2 m length and 0.6 mm in diameter, if the resistance of the wire is 50 Ω.

13.The resistance of an electric wire of an alloy is 10 Ω. If the thickness of wire is 0.001 meter, and length is 1 m, find its resistivity.

14.The resistivity of a metal wire is 10 x 10−8 Ω m at 20°C. Find the resistance of the same wire of 2 meter length and 0.3 mm thickness.

15.The area of cross section of wire becomes half when its length is stretched to double. How the resistance of wire is affected in new condition?

16.A wire of length 3 m and area of cross-section 1.7 × 10-6 m2 has a resistance 3 × 10-2 ohm.
a. What is the formula for resistivity of the wire and what is the unit of it
b. Calculate the resistivity of the wire

17.There are m resistor each of resistance R. First they all are connected in series and equivalent resistance is X. Now they are connected in parallel and equivalent resistance is Y.  What is the ratio of X and Y?

18.Compute the resistivity of the given material whose resistance is 2 Ω; area of cross-section and length are 25cm2 and 15 cm respectively?

19 The length and area of wire are given as 0.2 m and 0.5 m2 respectively. The resistance of that wire is 3 Ω, calculate the resistivity?

20.An electrician wishes to cut a copper wire (ρ=1.724∗10−8Ωm) that has no more than 10Ω of resistance. The wire has a radius of 0.725mm. Approximately what length of wire has a resistance equal to the maximum 10Ω ?

21 What is the resistance of a 100m length of round copper wire with a radius of 0.3mm?
ρcopper=1.68⋅10−8Ωm 

22.Two students are performing a lab using lengths of wire as resistors. The two students have wires made of the exact same material, but Student B has a wire the has twice the radius of Student A's wire. If Student B wants his wire to have the same resistance as Student A's wire, how should Student B's wire length compare to Student A's wire?

23.What will be the resistivity of a metal wire of 2 m length and 0.6 mm in diameter, if the resistance of the wire is 50 Ω.

24.The resistance of an electric wire of an alloy is 10 Ω. If the thickness of wire is 0.001 meter, and length is 1 m, find its resistivity.

25.The resistivity of a metal wire is 10 x 10−8 Ω m at 20°C. Find the resistance of the same wire of 2 meter length and 0.3 mm thickness.

26.The area of cross section of wire becomes half when its length is stretched to double. How the resistance of wire is affected in new condition?


27. Calculate the resistance of a copper wire of length 2m and area of cross section 10-6 m². Resistivity of copper is 1.7 x 10-8 Ωm

28. A copper wire of length 2m and area of cross section 1.7 x 10-6 m2 has a resistance of 2 x 10-2 ohms. Calculate the resistivity of copper.

29.. The amount of charge passing through a cell in 12 seconds is 3C. What is the current supplied by the cell?

30. A 12 V battery of a car is connected across a 4 resistor. Calculate the current passing through the resistor.

31. Resistivity of a given copper wire of length 2m is 1.7 x 10-8 Ωm. The wire is stretched so that its length becomes 4m. Find new resistivity of the copper wire.

32.. Resistance of a given wire of length ‘L’ is 3Ω. The wire is stretched uniformly such that its length becomes 2L. Find the new resistance of the stretched wire.

33.. Resistance of a given wire of length ‘L’ is 4Ω. The wire is stretched uniformly such that its length becomes 3L. Find the new resistance of the stretched wire.

34.. A copper wire has a diameter of 0.5 mm and resistivity of 1.6 x 10-8 Ωm. What will be the length of this wire to make its resistance 10Ω? How much does the resistance change if the diameter is doubled?

35.. A 6Ω resistance wire is doubled up by folding Calculate the new resistance of the wire.

36.. Calculate the resistance of an aluminium cable of length 10km and diameter 20mm if the resistivity of aluminum is 2.7 x 10-8 Ωm

37.. Calculate the area of cross section of a wire if its length is 1.0m, its resistance is 23Ω and the resistivity of the material of the wire is 1.84 x 10-6 Ωm

38. A piece of wire of resistance 20Ω is drawn out so that its length is increased to twice its original length Calculate the resistance of the wire in the new situation

39. Two cylindrical wires of the same material have their lengths in the ratio of 4 : 9. What should be the ratio of their radii so that their resistances are in the ratio of 4:1?

40. Two wires of the same metal, have the same area of cross section but their lengths in the ratio of 3 : 1. What should be the ratio of current flowing through them respectively, when the same potential difference is applied across each of their length?

41.Two wires A and B of length 30m and 10m have radii 2cm and lcm respectively. Compare the resistances of the two wires. Which will have less resistance?