An oceanographer is testing a high-power heated probe designed for deep-sea temperature regulation, rated at 150 V150\text{ V}150 V, 500 W500\text{ W}500 W.
The probe's heating core is constructed from a length of constantan alloy wire wound in a spiral groove around a quartz cylinder of length 24 cm24\text{ cm}24 cm and diameter 2.0 cm2.0\text{ cm}2.0 cm. The distance between the centres of adjacent turns of the wire is 1.5 mm1.5\text{ mm}1.5 mm.
To determine which reel of wire from the workshop shelf was used, the technician looks at the imperial standard wire gauge (swg) on the reels.
The data sheet provides the following information:
- resistivity of constantan alloy at operating temperature = 4.9×10−7 Ω m4.9 \times 10^{-7}\ \Omega\text{ m}4.9×10−7 Ω m
| swg | 24 | 26 | 28 | 30 | 32 |
|---|---|---|---|---|---|
| diameter of wire / 10−3 m10^{-3}\text{ m}10−3 m | 0.56 | 0.46 | 0.38 | 0.32 | 0.27 |
| cross-sectional area / 10−6 m210^{-6}\text{ m}^210−6 m2 | 0.25 | 0.16 | 0.11 | 0.08 | 0.06 |
Show that the electrical resistance of the constantan wire in this probe is 45 Ω45\ \Omega45 Ω.
Show that the length of wire wound around the quartz cylinder is approximately 10 m10\text{ m}10 m.
Use the values from (i) and (ii) to determine the swg number of the wire used in the probe.