Question

when a potential difference of 2 V is applied the ends of a wire of 5m length,a current of 1A is found to flow through it .calculate

1.the resistance per unit length of the wire

2.the resistance of 2m length of the wire

3.the resistance across the ends of the wire if it is doubled on itself.

Answer 1

V = I R

R = V /I = 2/1 = 2 ohm

R = ρ L/A

R₁ /R₂ = L₁ /L_{2 (Put L2 = 1 m)}

2 /R₂ = 5 / 1

R₂ = 2/5 = 0.4 Ohm

Similarly you can find out for 2m length.

If wire is doubled, then it would mean that two halves of the resistance of the full wire are connected in parallel.

Resistance of half wire r = 2/2 = 1 ohm

In parallel

1/R = 1/r + 1/r = 1+1 = 2

R = 1/2 ohm = 0.5 ohm