Final answer:
The frequency of the voltage source is determined from the angular frequency in the cosinusoidal function. Steady-state current and phase difference in an RLC circuit involve calculating the total impedance and applying Ohm's Law. The total impedance is the vector sum of the resistive, capacitive, and inductive impedances.
Step-by-step explanation:
The frequency of a cosinusoidal voltage source can be determined directly from the given function v(t) = 2cos(4πt). The coefficient of t in the angular frequency ω (omega), which is 4π rad/s, allows us to find the frequency f using the relationship ω = 2πf. This results in a frequency of 2 Hz for the given voltage source.
The steady-state current in an RLC series circuit and the phase difference between voltage and current can be found by calculating the impedances of the individual components (the resistor, capacitor, and inductor), and then combining them to get the total circuit impedance. Once the total impedance is known, Ohm's Law (V=IZ) can be applied to determine the current.
The phase difference depends on the relative magnitudes of the reactances of the inductor and capacitor.
The total impedance of the RLC circuit is the vector sum of the individual impedances of the resistor (R), inductor (L), and capacitor (C), which can be represented in complex form. The power factor and energy usage are derived from the voltage, current, and phase angle.