An engineer is investigating a 24 V24\text{ V}24 V, 75 W75\text{ W}75 W heating element designed for a scientific instrument.
A length of constantan wire is wound in a spiral groove along 12.5 cm12.5\text{ cm}12.5 cm of a ceramic cylinder of diameter 0.80 cm0.80\text{ cm}0.80 cm. The distance between the centres of adjacent turns of the wire is 0.50 mm0.50\text{ mm}0.50 mm.
The reels of wire available in the laboratory are labelled with their standard wire gauge (swg). The engineer wishes to identify which reel holds the wire used in this heating element.
The engineering data book gives the following information:
- resistivity of constantan at operating temperature = 4.9×10−7 Ω m4.9 \times 10^{-7}\ \Omega\text{ m}4.9×10−7 Ω m
| swg | 20 | 21 | 22 | 23 | 24 |
|---|---|---|---|---|---|
| diameter of wire / 10−3 m10^{-3}\text{ m}10−3 m | 0.91 | 0.81 | 0.71 | 0.61 | 0.56 |
| cross-sectional area / 10−6 m210^{-6}\text{ m}^210−6 m2 | 0.65 | 0.52 | 0.40 | 0.29 | 0.25 |
Show that the resistance of the constantan wire wound on the ceramic cylinder is 7.68 Ω7.68\ \Omega7.68 Ω.
Show that the length of wire wound on the heating element is approximately 6.3 m6.3\text{ m}6.3 m.
Use the information given in (i) and (ii) to determine the swg number of the wire used as the heating element.