What is electrical resistivity ? Derive its SI unit, In a series electrical comprising a resistor made up of metallic wire, the ammeter reads , 100 mA. If the length of the wire is doubled, how will the current in the circuit change ? Justify your answer.

Explanation

Electrical resistivity of the material of a conductor is the resistance offered by the conductor of length 1 m and area of cross-section ` 1 m^(2)`. Numerically it is equal to the resistance of a rod of that substance which is 1 metre and 1 square metre in cross-section.
` p = (RA)'/l`
Since unit of R = Ohm, A= `("metre")^(2)` , l = (metre)
Unit of resistivity , p = `( " ohm" xx (" metre")^(2)")/("(metre)") ` = ohm-metre (or ` Omega` m)
` R= (pl)/A`
if l= 2l
New resitance ,` R' = (pl)/A= ( p xx 2l)/A = (2pl)/A`
R = 2R
I = ? V= V
V = IR .....[ Ohm's law ` Rightarrow I = V/R Rightarrow I' = V/R`
V =V , R = 2 R
` I = V/(2R) " " Rightarrow I= 1/2 xx I `
I = 100 mA ` Rightarrow I = 1/2 xx 100 = 50 mA`
Current in the circuit is reduced to half.