An RC circuit is an electrical circuit with a resistor, R, and a capacitor, C, as shown in Fig. 7.12. If the input voltage, V(t),

is a given oscillating function of time (t, in units of s), such as V(t) = V0 cos(ωt), the voltage difference across the capacitor (i.e., the output voltage) is given by the real part of V¯, where V¯(t) = V0e iωt 1 + iωRC .

a. What are the units of V0? What are the units of ω? Show that ωRC is dimensionless, as it must be.

b. What is the real part of V¯(t)?

c. Set V0 = 1 V, ω = 1 s−1 and R = 1 Ω. Plot the output voltage as a function of t, for C = 0, 2, 4 F. What effect does the capacitance have on the output?