Worksheet: Electrical Conductivity and Resistivity

In this worksheet, we will practice calculating the electrical resistance of a material given its resistivity, cross-sectional area, and length.

Q1:

A 1 . 0 × 1 0 2 V potential difference is applied across a 10.0-m length of wire with a diameter of 4.621 mm. The magnitude of the current density produced is 2 . 0 × 1 0 8 A/m2. What is the resistivity of the wire?

  • A 4 . 5 × 1 0 8 Ω⋅m
  • B 4 . 2 × 1 0 8 Ω⋅m
  • C 5 . 4 × 1 0 8 Ω⋅m
  • D 5 . 0 × 1 0 8 Ω⋅m
  • E 5 . 8 × 1 0 8 Ω m

Q2:

What is the resistivity of a 5-gauge wire (cross-sectional area of 1 6 . 8 × 1 0 6 m2) of 5.00 m length, and 5.00 Ω resistance?

  • A 1 . 4 9 × 1 0 8 Ω⋅m
  • B 1 . 3 7 × 1 0 8 Ω⋅m
  • C 1 . 6 6 × 1 0 8 Ω⋅m
  • D 1 . 7 1 × 1 0 8 Ω⋅m
  • E 1 . 8 0 × 1 0 8 Ω⋅m

Q3:

Find the resistance of a 20.0-m-long piece of copper wire that has a 2.053-mm diameter. Use a value of 1 . 5 9 × 1 0 8 Ω⋅m for the resistivity of copper.

Q4:

A coaxial cable consists of an inner conductor with radius of 0.2500 cm and an outer radius of 0.5000 cm. The cable has a length of 10.0 metres. Plastic with a resistivity of Ω⋅m separates the two conductors. What is the resistance of the cable?

  • A Ω
  • B Ω
  • C Ω
  • D Ω
  • E Ω

Q5:

A resistor is made from a hollow cylinder of carbon, as shown. The inner radius of the cylinder 𝑅 = 0 . 2 0 1 mm and the outer radius 𝑅 = 0 . 3 0 2 mm. The length of the resistor 𝐿 = 0 . 9 0 mm. The resistivity of the carbon is 𝜌 = 3 . 5 × 1 0 5 Ω⋅m. What is the resistance of the resistor?

Q6:

Coils are often used in electric and electronic circuits. A particular coil is formed by winding 500 turns of insulated 30 gauge copper wire in a single layer on a cylindrical non-conducting core of radius 1.00 mm. The wire’s cross-sectional area is 0.0510 mm2, which includes the negligible area of the insulation. Find the resistance of the coil. Use a value of 1 . 6 8 × 1 0 8 Ω⋅m for the resistivity of copper.

Q7:

A wire with a resistance of 8.0 Ω is drawn out through a die so that its new length is three times its original length. The density and resistivity of the wire’s constituent material are not changed by the stretching process. Find the resistance of the wire after it has been stretched.

Q8:

Consider two cables, one made of copper and one made of aluminum. Both are 15.00 m long, and the copper cable has a resistance of 0.035 Ω. In determining the electrical and mechanical properties of the cables, use a value of 8 9 6 0 kg/m3 for the density of copper and 1 . 6 8 × 1 0 8 Ω⋅m for its resistivity. Use a value of 2 7 6 0 kg/m3 for the density of aluminum and 2 . 6 5 × 1 0 8 Ω⋅m for its resistivity.

What is the weight of the copper cable?

What is the weight of the aluminum cable?

What is the resistance of the aluminum cable?

Q9:

A wire is drawn through a die, stretching it to double its original length. By what factor is the wire’s resistance increased after stretching?

Q10:

A rod of pure silicon is used in a particle detector. The rod is 18.0 cm long and has a diameter of 3.00 cm. Find the current through the rod when a potential difference of 1 . 3 0 × 1 0 3 V is applied across its length. Use a value of 2 3 0 0 Ω⋅m for the resistivity of pure silicon.

Q11:

A steel rod has a length of 22.00 cm and a resistance of 3.00 µΩ. Find the radius of the rod. Use a value of 2 0 . 0 0 × 1 0 8 Ω⋅m for the resistivity of steel.

Q12:

The diameter of an aluminum wire is 10 mm. Find the resistance of a 0.56 kilometers length of such wire used for power transmission. Use a value of 2 . 6 5 × 1 0 8 Ω⋅m for the resistivity of aluminum.

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