A potentiometer is a variable resistor with three terminals. Figure 6.12a shows a potentiometer connected to a voltage source. The two end terminals are labeled as 1 and 2, and the adjustable terminal is labeled as 3 . The potentiometer acts as a voltage divider, and the total resistance is separated into two parts, as shown in Figure 6.12b, where \(R_{13}\) is the resistance between terminal 1 and terminal 3 , and \(R_{32}\) is the resistance between terminal 3 and terminal 2. Determine the relationship between the input voltage \(v_{\mathrm{i}}\) and the output voltage \(v_{\mathrm{o}}\).

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Vi (a) 2 FIGURE 6.12 Problem 5: (a) Potentiometer and (b) voltage divider. V (b) 813 R32