Final answer:
To calculate vo(t) in the given circuit, which consists of a resistor connected in series with a capacitor, we need to determine the voltage across the capacitor. The voltage across a capacitor in an AC circuit is given by Vc(t) = Vc0 * cos(ωt + φ), where Vc0 is the amplitude of the voltage and ω is the angular frequency. By substituting the given values into the equation, we can find the expression for vo(t).
Step-by-step explanation:
The given circuit consists of a resistor (R) connected in series with a capacitor (C). To calculate vo(t), we need to determine how the voltage across the capacitor changes with time. The voltage across a capacitor in an AC circuit is given by:
Vc(t) = Vc0 * cos(ωt + φ)
where Vc(t) is the voltage across the capacitor at time t, Vc0 is the amplitude of the voltage, ω is the angular frequency, t is the time, and φ is the phase angle. In this case, Vc0 = Vo = 100 V and ω = 200 rad/s. Since the given equation for vo(t) is in terms of cos, we can assume that the phase angle φ is 0.
Therefore, the expression that represents the output voltage of the circuit is:
vo(t) = Vc0 * cos(ωt) = 100 * cos(200t) V