Question

After plotting the voltage waveform, obtain expressions and generate plots for i(t),p(t), and w(t) for a 0.2mF capacitor. The voltage waveforms are given by

(a) v ₁(t)=5r(t)−5r(t−2)V

Answer 1

The output current for an AC voltage source varies depending on whether it is connected across a capacitor, an inductor, or a resistor. The phase of the current is determined by the type of component: leading for capacitive loads and lagging for inductive ones

Step-by-step explanation:

When calculating the output current for an AC voltage source across different components, one must consider the properties of the elements in the circuit. For a capacitive or inductive load, the current will be out of phase with the voltage, while for a resistive load, the current and voltage will be in phase. We use the voltage expression v(t) = Vo sin(ωt), where Vo = 100 V and ω = 2007 rad/s to calculate the current:

• For a 20-μF capacitor, the capacitive reactance XC = 1/(ωC) is used to find the current amplitude Io with Io = Vo/XC.
• For a 20-mH inductor, the inductive reactance XL = ωL is used similarly to find the current amplitude.
• For a 50-Ω resistor, Ohm's law I = V/R directly provides the current amplitude.

The phase relationship between the current and voltage depends on whether the circuit is capacitive (current leads) or inductive (current lags).