Electricity Worksheet5

The resistance of a wire of length 80 cm and of uniform area of crosssection 0.025 cm^{2}, is found to be 1.50 ohm. Calculate the resistivity of the wire.

Calculate the resistance of 1 km long copper wire of radius 1 mm. Resistivity of copper is 1.72 × 10^{–8} Ω m.

Two copper wires A and B of length 30 m and 10 m have radii 2 cm and 1 cm respectively. Compare the resistances of the two wires. Which will have less resistance?

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

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

A negligibly small current is passed through a wire of length 15 m and of uniform crosssection 6.0 10^{–7} m^{2} and its resistance is measured to be 5.0Ω. What is the resistivity of the material at the temperature of the experiment?

A metal wire of resistivity 64 10^{–6} ohm cm and length 198 cm has a resistance of 7Ω. Calculate its radius.

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

The resistivity of copper is 1.76 × 10^{–8} ohm m. The radius of the wire is 1 mm. Calculate the length of a telegraph wire needed for having a resistance of 10.5 Ω.

A resistance wire made from German silver has a resistance of 4.25 Ω. Calculate the resistance of another wire made from the same material such that its length increases by 4 times and area of crosssection decreases by 3 times.
Answer:

length of the wire, l = 80 cm
Crosssectional area of the wire, A = 0.025 cm^{2}
Resistance of the wire, R = 1.50 Ω
As ohm cm

Length of the wire, l = 1 km = 1000 m
Radius of the wire, r = 1 mm = 10^{–3 }m, resistivity of copper,
Crosssectional area of the wire,

Let the two resistances be labeled as R_{1} and R_{2}.
Here,
As
and
Thus,
Clearly, R_{1} < R_{2}

.
When the wire of length l and crosssectional area A is doubled on it, its length becomes l/2 and crosssectional area becomes 2A.
New resistance of the wire,



= 0.024 cm

As

