(a) The instantaneous source voltage can be determined by using the given magnitude and phase angle. Since the phase angle is 0°, the instantaneous source voltage can be written as:
V(t) = 277 * cos(2π * 60 * t)
(b) For a 30-Ω resistor, the current entering the positive terminal is the same as the source current. Since the voltage and resistance are given, we can use Ohm's law to determine the current:
I(t) = V(t) / R = (277 * cos(2π * 60 * t)) / 30
(c) For a 15-mH inductor, the phasor current can be determined using the formula:
I = V / jωL
where j is the imaginary unit (√(-1)), ω is the angular frequency (2π * frequency), and L is the inductance. In this case, ω = 2π * 60 and L = 15 * 10^(-3):
I = (277 ∠0°) / (j * 2π * 60 * 15 * 10^(-3))
To find the instantaneous current, we can take the real part of the phasor current and then convert it to the time-domain using cosine function:
I(t) = Re(I * e^(jωt))
(d) For a capacitor with 100 mF, the phasor current can be determined using the formula:
I = jωCV
where C is the capacitance. In this case, ω = 2π * 60 and C = 100 * 10^(-3):
I = (j * 2π * 60 * 100 * 10^(-3)) * 277 ∠0°
To find the instantaneous current, we can take the imaginary part of the phasor current and then convert it to the time-domain using sine function:
I(t) = Im(I * e^(jωt))