# Passive Transducers

passive transducer is a transducer, which produces the variation in passive element. We will consider the passive elements like resistor, inductor and capacitor. Hence, we will get the following three passive transducers depending on the passive element that we choose.

• Resistive Transducer
• Inductive Transducer
• Capacitive Transducer

Now, let us discuss about these three passive transducers one by one.

## Resistive Transducer

A passive transducer is said to be a resistive transducer, when it produces the variation (change) in resistance value. the following formula for resistance, R of a metal conductor.

$$R=\frac{\rho \:l}{A}$$

Where,

$\rho$ is the resistivity of conductor

$l$ is the length of conductor

$A$ is the cross sectional area of the conductor

The resistance value depends on the three parameters $\rho, l$ & $A$. So, we can make the resistive transducers based on the variation in one of the three parameters $\rho, l$ & $A$. The variation in any one of those three parameters changes the resistance value.

• Resistance, R is directly proportional to the resistivity of conductor, $\rho$. So, as resistivity of conductor, $\rho$ increases the value of resistance, R also increases. Similarly, as resistivity of conductor, $\rho$ decreases the value of resistance, R also decreases.

• Resistance, R is directly proportional to the length of conductor, $l$. So, as length of conductor, $l$ increases the value of resistance, R also increases. Similarly, as length of conductor, $l$ decreases the value of resistance, R also decreases.

• Resistance, R is inversely proportional to the cross sectional area of the conductor, $A$. So, as cross sectional area of the conductor, $A$ increases the value of resistance, R decreases. Similarly, as cross sectional area of the conductor, $A$ decreases the value of resistance, R increases.

## Inductive Transducer

A passive transducer is said to be an inductive transducer, when it produces the variation (change) in inductance value. the following formula for inductance, L of an inductor.

$L=\frac{N^{2}}{S}$Equation 1

Where,

$N$ is the number of turns of coil

$S$ is the number of turns of coil

the following formula for reluctance, S of coil.

$S=\frac{l}{\mu A}$Equation 2

Where,

$l$ is the length of magnetic circuit

$\mu$ is the permeability of core

$A$ is the area of magnetic circuit through which flux flows

Substitute, Equation 2 in Equation 1.

$$L=\frac{N^{2}}{\left (\frac{l}{\mu A} \right )}$$

$\Rightarrow L=\frac{N^{2}\mu A}{l}$Equation 3

From Equation 1 & Equation 3, we can conclude that the inductance value depends on the three parameters $N,S$ & $\mu$. So, we can make the inductive transducers based on the variation in one of the three parameters $N,S$ & $\mu$. Because, the variation in any one of those three parameters changes the inductance value.

• Inductance, L is directly proportional to square of the number of turns of coil. So, as number of turns of coil, $N$ increases the value of inductance, $L$ also increases. Similarly, as number of turns of coil, $N$ decreases the value of inductance, $L$ also decreases.

• Inductance, $L$ is inversely proportional to reluctance of coil, $S$. So, as reluctance of coil, $S$ increases the value of inductance, $L$ decreases. Similarly, as reluctance of coil, $S$ decreases the value of inductance, $L$ increases.

• Inductance, L is directly proportional to permeability of core, $\mu$. So, as permeability of core, $\mu$ increases the value of inductance, L also increases. Similarly, as permeability of core, $\mu$ decreases the value of inductance, L also decreases.

## Capacitive Transducer

A passive transducer is said to be a capacitive transducer, when it produces the variation (change) in capacitance value. the following formula for capacitance, C of a parallel plate capacitor.

$$C=\frac{\varepsilon A}{d}$$

Where,

$\varepsilon$ is the permittivity or the dielectric constant

$A$ is the effective area of two plates

$d$ is the effective area of two plates

The capacitance value depends on the three parameters $\varepsilon, A$ & $d$. So, we can make the capacitive transducers based on the variation in one of the three parameters$\varepsilon, A$ & $d$. Because, the variation in any one of those three parameters changes the capacitance value.

• Capacitance, C is directly proportional to permittivity, $\varepsilon$. So, as permittivity, $\varepsilon$ increases the value of capacitance, C also increases. Similarly, as permittivity, $\varepsilon$ decreases the value of capacitance, C also decreases.

• Capacitance, C is directly proportional to the effective area of two plates, $A$. So, as effective area of two plates, $A$ increases the value of capacitance, C also increases. Similarly, as effective area of two plates, $A$ decreases the value of capacitance, C also decreases.

• Capacitance, C is inversely proportional to the distance between two plates, $d$. So, as distance between two plates, $d$ increases the value of capacitance, C decreases. Similarly, as distance between two plates, $d$ decreases the value of capacitance, C increases.

In this chapter, we discussed about three passive transducers. In next chapter, let us discuss about an example for each passive transducer.