Question

wire of length one metre and area of cross section 2 mm² is connected with a battery of 4volt a current of 8amp flows in it then find the resistivity of wire
​

Answer 1

Given :

▪ Length of wire = 1m

▪ Area of cross section = 2mm²

▪ Current flow = 8A

▪ Voltage of battery = 4V

To Find :

▪ Resistivity of wire.

Concept :

→ As per ohm's law, current passing through a conductor is directly proportional to the applied potential difference. (at constant temperature)

$\star\bf\:\:V\varpropto I\\ \\ \star\bf\:\:V=I\times R$

• V denotes pd
• I denotes current
• R denotes resistance of conductor

→ Resistivity is materialistic property of the conductor, it doesn't depend on the length/area of cross section or other dimensions of conductor.

→ Resistance of a conductor is directly proportional to the length and indirectly proportional to the area of cross section of conductor.

$\star\bf\:\:R\varpropto\dfrac{L}{A}\\ \\ \star\bf\:\:R=\dfrac{\rho\times L}{A}$

Conversion :

☢ 1mm = 10$^{-3}$m

☢ 1mm² = 10$^{-6}$m²

Calculation :

$\dashrightarrow\rm\:V=I\times R\\ \\ \dashrightarrow\rm\:V=I\times \dfrac{\rho\times L}{A}\\ \\ \dashrightarrow\rm\:4=8\times \dfrac{\rho\times 1}{10^{-6}}\\ \\ \dashrightarrow\rm\:\rho=\dfrac{4\times 10^{-6}}{8}\\ \\ \dashrightarrow\underline{\boxed{\tt{\purple{\rho=5\times 10^{-7}\:\Omega\:m}}}}\:\orange{\bigstar}$