Question 6.2.4: Assuming the potentiometer resistance R1 is proportional to ......

System Dynamics
System Dynamics [1255330]

Assuming the potentiometer resistance ${{R}}_{1}$ is proportional to x, derive the expression for the output voltage ${{v}}_{o}$ as a function of x.

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The length of the pot is L and its total resistance is ${{R}}_{1}$ + ${{R}}_{2}$ . Figure 6.2.5b shows the circuit diagram of the system. From the voltage-divider rule,

$v_{o}={\frac{R_{1}}{R_{1}+R_{2}}}V$ (1)

Because the resistance ${{R}}_{1}$ proportional to x,

R_{1}=(R_{1}+R_{2})\left(\frac{x}{L}\right)

Substituting this into equation (1) gives

v_{o}={\frac{x}{L}}V=K x

where K = V/L is the gain of the pot.

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