Question

A manganese wire has a diameter of 1 mm and resistance of 15 ohm What is the resistance of
a manganese wire having a diameter of 3mm sq. but of a same length​

Answer 1

Question - A manganese wire has a diameter of 1 mm and resistance of 15 ohm. What is the resistance of

a manganese wire having a diameter of 3mm but of a same length​?

Answer - Resistance of wire for given diameter is - 1.6 ohm

Resistance of a material is defined as obstruction to flow of charge.

Resistance is calculated by the formula -

R = rho*l/a

R represents resistance, rho is resistivity, l is for length and a is for cross sectional area.

Formula for area is πr² where r is radius.

Since wire is of manganese in both the cases, resistivity will be same and length is same is given in question.

Hence, R1A1 = R2A2

R1 = 15 ohm

A1 = π (1/2)²

A1 = 0.5²π

R2 to be calculated

A2 = π (3/2)²

A2 = π(1.5)²

Keeping values in formula -

R2 = R1*A1/A2

R2 = 15*0.5²/1.5²

R2 = 1.6 ohm

Thus, resistance of manganese wire for 3mm diameter will be 1.6 ohm