Question

If you have a copper wire resistor with resistivity rho = 1.68 Times 10^-8 Ohm m. how long would it have to be to give you a resistance of 100 Ohm. if it has a circular cross-section with radius 0.1 mm? Suppose you have a copper wire with a radius 0.8 mm. what is the resistance for a one meter length of wire? For two resistors R_1 = 1.15 k Ohm and R_2 = 10.3K Ohm. what would be the equivalent resistance if we add these in series? In parallel?

Answer 1

The resistance of a wire is given by the formula R = rho * L / A, where R is the resistance, rho is the resistivity, L is the length of the wire and A is the cross-sectional area of the wire. The cross-sectional area of a wire with a circular cross-section and radius r is given by A = pi * r^2.

For a copper wire with resistivity rho = 1.68 * 10^-8 Ohm m and a circular cross-section with radius 0.1 mm, to have a resistance of 100 Ohm, the length of the wire would have to be L = R * A / rho = 100 Ohm * (pi * (0.1 mm)^2) / (1.68 * 10^-8 Ohm m) = 0.187 meters.

For a copper wire with a radius of 0.8 mm and a length of one meter, the resistance would be R = rho * L / A = (1.68 * 10^-8 Ohm m) * (1 m) / (pi * (0.8 mm)^2) = 0.0000835 Ohm.

For two resistors R_1 = 1.15 kOhm and R_2 = 10.3 kOhm in series, the equivalent resistance would be R_eq = R_1 + R_2 = 11.45 kOhm.

For two resistors R_1 = 1.15 kOhm and R_2 = 10.3 kOhm in parallel, the equivalent resistance would be R_eq = 1 / (1/R_1 + 1/R_2) =1.06 kOhm.