Question

A nichrome wire is 15 cm long and has a diameter of 0.25 ??.

a) What is its resistance?

b) If a 3.0 V battery is connected across the wire, how much current flows?

A wire is 0.4 m long and has a diameter of 1.2 × 10−4 ?. When a 3.0 V battery is connected across the wire, a current of 2.0 × 10−3 ? flows. Determine:

c) the resistance of the wire

d) the resistivity of the wire

Answer 1

Part 1

a) length, l = 15 cm = 0.15 m

diameter, d = 0.25 mm = 2.5 x 10^-4 m

resistivity, = 1.1 x 10^-6 Ω m

resistance, R = l/A

R = l/r2

R = 4l/d2

R = (4 x 1.1 x 10^-6 x 0.15)/(3.14 x (2.5 x 10^-4)2)

R = 3.36 Ω

b) Voltage, V = 3V

current, I = V/R

I = 3/3.36

I = 0.89 A

Part 2

length, l = 0.4 m

diameter, d = 1.2 × 10⁻⁴ ?

voltage, V = 3.0 V

current, I = 2.0 × 10⁻³ A

c) Resistance, R = V/I

R = 3/(2 x 10^-3)

R = 1500 Ω

d) Resistivity, = RA/l

= Rd2/4l

= (1500 x 3.14 x (1.2 x 10^-4)²)/(4 x 0.4)

= 4.24 x 10^-5 Ωm