Numericals based on Resistivity

Numerical Problems

Q.1. 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

Q.2. 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.

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

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

Q.5. 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.

Q.6. 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.

Q.7. 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.

Q.8. 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?

Q.9. A 6Ω resistance wire is doubled up by folding Calculate the new resistance of the wire.

Q.10. 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

Q.11. 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

Q.12. 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

Q.13. 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?

Q.14. 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?

Q.15. 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?

Q.16. Calculate the resistance of 1 km long copper wire of radius 1 mm. Resistivity of copper is 1.7 x 10^-8 Ωm

Q.17. A 4Ω wire is doubled on it. Calculate the new resistance of the wire.

Q.18. What should be the length of the nichrome wire of resistance 4.5Ω, if the length of a similar wire is 60cm and resistance 2.5Ω?

Q.19. A metal wire of resistivity 64 x 10^-6 Ωm and length 198cm has a resistance of 7Ω. Calculate its radius.

Q.20. Calculate the resistivity of the material of a wire 1.0m long. 0.4mm in diameter and having a resistance of 2.0Ω.

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