10.4: Resistive Sensors

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Sensors may be made from capacitive, inductive, or resistive materials. These sensors may involve direct energy conversion or may involve multiple energy conversion processes. In Chapters 2 and 3 capacitive energy conversion devices were discussed. The capacitance \(C\) of a parallel plate capacitor is given by

\[C= \frac{\epsilon A}{d_{thick}}. \nonumber \]

If the permittivity \(\epsilon\), cross sectional area \(A\), or separation of the plates \(d_{thick}\) change with respect to any effect, we can make a capacitive sensor. Capacitive sensors are calibrated devices which involve energy conversion between electricity and material polarization. While most inductive energy conversion devices are outside the scope of this book, a few such devices were discussed in Chapters 4 and 5. The inductance \(L\) of a single turn inductor is given by

\[L= \frac{\mu d_{thick}}{w}. \nonumber \]

If the permeability \(\mu\), thickness \(d_{thick}\), or width \(w\) change with respect to any effect, we can make an inductive sensor which utilizes energy conversion between electricity and magnetic energy. Similarly, the resistance \(R\) of a uniform resistive device is given by

\[R= \frac{\rho l}{A}. \nonumber \]

If the resistivity \(\rho\), length \(l\), or cross sectional area \(A\) change with respect to any effect, we can make a resistive sensor. When a current is applied through a resistive sensor, energy is converted from electricity to heat, and a resistive sensor is calibrated so that a given voltage drop corresponds to a known change in some parameter.

Many resistive senors are available. A potentiometer is a variable resistor. As current flows through it, energy is converted from electricity to heat. When the knob of a potentiometer is turned, the length of the material through which the current flows is changed, so the rate of energy conversion through the device changes. A resistance temperature detector converts a temperature difference to electricity [37, p. 88]. Resistance temperature detectors work based on the idea of the Thomson effect discussed in Section 8.5.1. In these devices, the resistivity varies with temperature. When a strain is applied to a resistive strain gauge, both the length and cross sectional area of the device change. Pirani hot wire gauges are used to measure pressure in low pressure environments [37, p. 97]. In a Pirani gauge, current is applied through a metallic filament, and the filament heats up. As air molecules hit the filament, heat is transferred away from it. The resistance of the filament depends on temperature, and the filament cools more quickly in an environment with more air molecules than in an environment at a lower pressure. By monitoring the resistance of the filament, the pressure can be determined.