Electricity Worksheet-5

Electricity Worksheet-5

 

  1. The resistance of a wire of length 80 cm and of uniform area of cross-section 0.025 cm2, is found to be 1.50 ohm. Calculate the resistivity of the wire.

 

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

 

  1. 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?

 

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

 

  1. 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?

 

  1. A negligibly small current is passed through a wire of length 15 m and of uniform cross-section 6.0  10–7 m2 and its resistance is measured to be 5.0Ω. What is the resistivity of the material at the temperature of the experiment?

 

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

 

  1. 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.

 

  1. 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.

 

  1. 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 cross-section decreases by 3 times.

 

Answer:

  1. length of the wire,  l = 80 cm

Cross-sectional area of the wire, A = 0.025 cm2

Resistance of the wire, R = 1.50 Ω

As ohm cm

 

  1. Length of the wire, l = 1 km = 1000 m

Radius of the wire, r = 1 mm = 10–3 m, resistivity of copper,

Cross-sectional area of the wire,

 

 

  1. Let the two resistances be labeled as R1 and R2.

Here,        

                  

As              

and           

Thus,        

Clearly, R1 < R2

 

  1. .

When the wire of length l and cross-sectional area A is doubled on it, its length becomes l/2 and cross-sectional area becomes 2A.

New resistance of the wire,

 

 

 

= 0.024 cm

 

  1. As