Question

Nichrome wire, often used for heating elements, has resistivity of 1.0 × 10-6 Ω • m at room temperature. What length of No. 30 wire (of diameter 0.250 mm) is needed to wind a resistor that has 50 ohms at room temperature?

Answer 1

Length of wire will be 2.45 m

Step-by-step explanation:

We have given resistivity of the wire
`\rho =10^(-6)ohm-m`

Diameter d= 0.25 mm

So radius
`r=(d)/(2)=(0.25)/(2)=0.125mm=0.125* 10^(-3)m`

Area
`A=\pi r^2=3.14* (0.125* 10^(-3))^2=4.9* 10^(-8)m^2`

Resistance of wire = 50 ohm

We know that resistance is given by
`R=(\rho l)/(A)`

So
`50=(10^(-6)l)/(4.9* 10^(-8))`

`l=2.45m`

So length of wire will be 2.45 m