The circuit shown in Figure P26 consists of a resistor and a capacitor and is thus called an RC circuit. If we apply a sinusoidal voltage υi, called the input voltage, to the circuit as shown, then eventually the output voltage !o will be sinusoidal also, with the same frequency but with a different amplitude and shifted in time relative to the input voltage. Specifically , if υi = Ai sin (t, then υo = Ao sin(ωt + ϕ). The frequency–response plot is a plot of Ao /Ai versus frequency ω. It is usually plotted on logarithmic axes.
Upper-level engineering courses explain that for the RC circuit shown, this ratio depends on ω and RC as follows:
where s = ωi. For RC = 0.1 s, obtain the log-log plot of versus ω and use it to find the range of frequencies for which the output amplitude Ao is less than 70 percent of the input amplitude Ai.
Figure P26
