The electrical resistance of a circuit is the ratio between the voltage applied to the current flowing through it.
According to Ohm’s law, there is a relation between the current flowing through a conductor and the potential difference across it. It is given by,
V ∝ I V = IR
- V = Potential difference measured across the conductor (in volts)
- I = Current through the conductor (in amperes)
- R = Constant of proportionality called resistance (in ohms)
First consider that wire is doubled on it means to fold the length of wire. That is its length will get half and area of cross-section will get doubled.
∴ Let the resistance of the wire originally ‘R’ of length ‘L’ and area of cross-section ‘A’ with resistivity of material is ‘p’, Then
R = p l/A = 4 Ω
Now, for new arrangement,
p’ = p
l’ = l / 2
A’ = 2A
R’ = p’ l’/A’ = p (l /2) ÷ 2A
R’ = 1/4 (p l / A)
R’ = 1/4R
R’ = 1/4 × 4
R’ = 1Ω.
For additional information on resistance and Ohm’s Law, refer to the video