A potential difference of 13 V is found to produce a current of 0.37 A in a 3.1 m length of wire with a uniform radius of 0.42 cm.(a) What is the resistance of the wire? (b) What is the resistivity of the wire? Please show work.
Voltage (Volts) = Current (Amps) times Resistance (Ohms) or V=IxR = R = V/I = 13/0.37 = 35.14 Ohms Resistance = Resistivity * Length/Area The longer the wire is, the more resistance it has. The larger the crossectional area of the wire (pi times radius^2), the less resistance it has Longer wires have more resistance, thicker wires have less 35.14 = Resistivity * 3.1/pi*0.0042^2 Resistivity = 35.14*pi*0.0042^2/3.1 = 6.281 x 10^-4
P. D. applied = V = 13 V Current produced = I = 0.37 A (a) Resistance of the wire = R = V / I = 13/0.37 = 35.14 Ohm (b) R = ρL/A = (ρL) / π r?) = ρ = (R A) / L = R (π r?) / L ......... (1) R = Resistance of the wire = 35.14 Ohm , L = length of the wire = 3.1 m A = Area of cross-section of the wire = π r? r = radius of cross-section of the wire = 0.42 cm = 0.0042 m ρ = Resistivity of the wire in Ohm-m Substitute the values in the formula (1) and calculate. Take π = 3.14
