Question

A ribbon of nichrome (resistivity = 1.00 × 10-6 Ω·m) with a rectangular cross sectional area of (0.25 mm × 1.00 mm) will be used as a heating element in a toaster. How long should this ribbon be, if the total resistance is intended to be 1.5 Ω?
1.24 cm
2.79 cm
37.5 cm
12.4 cm
21.9 cm

Answer 1

The cross-sectional area of the ribbon in square meters is given by
\[c.s.a=0.25\times 10^{-3}\times 1.00\times 10^{-3}\]
The required resistance is given by
\[resistance=\frac{resistivity \times length}{c.s.a.}\]
\[1.5=\frac{1.00\times 10^{-6}\times l}{0.25\times 10^{-3}\times 1.00\times 10^{-3}}\]
from which we get
\[l=1.5\times 0.25\times 100=?\ cm\]