The resistance of a practical resistor depends on the nominal resistance and the

Chapter 2, Problem P 2.4-9

(choose chapter or problem)

The resistance of a practical resistor depends on the nominal resistance and the resistance tolerance as follows:

                              \(R_{\text {nom }}\left(1-\frac{t}{100}\right) \leq R \leq R_{\text {nom }}\left(1+\frac{t}{100}\right)\)

where \(R_{\text {nom }}\) is the nominal resistance and t is the resistance tolerance expressed as a percentage. For example, a \(100-\Omega\), 2 percent resistor will have a resistance given by

                               \(98 \Omega \leq R \leq 102 \Omega\)

The circuit shown in Figure P 2.4-9 has one input, \(v_{\mathrm{s}}\), and one output, \(v_{\mathrm{o}}\). The gain of this circuit is given by

                              gain = \(\frac{v_{\mathrm{o}}}{v_{\mathrm{s}}}=\frac{R_2}{R_1+R_2}\)

Determine the range of possible values of the gain when \(R_1\) is the resistance of a 100- \(\Omega\), 2 percent resistor and \(R_2\) is the resistance of a \(400-\Omega\), 5 percent resistor. Express the gain in terms of a nominal gain and a gain tolerance.