Final answer:
To find the steady-state current and resonance frequency of an RLC circuit, utilize the formulas for inductive and capacitive reactance, impedance, and Ohm's law. At resonance, impedance equals resistance, and the steady-state current calculation simplifies.
Step-by-step explanation:
To find the steady-state current (I(t) in an RLC series circuit with a voltage source E(t) = 18cos(20t)V, a resistor of 60Ω, an inductor of 2 H, and a capacitor of 50 μF (since 1100⁻¹ ≈ 0.00005 F or 50 μF), we first need to determine the circuit's reactance and impedance.
The inductive reactance (X) is given by X = 2πfL, the capacitive reactance (X) is given by X = 1/(2πfC), and the impedance (Z) is given by Z = √(R² + (X - X)²). However, to find the current at the resonance frequency, we must realize that at resonance, X = X, and the impedance is purely resistive (Z = R).
The resonance frequency (f) of an RLC circuit is f = 1/(2π√(LC)). Plugging in the given values, we can calculate the resonance frequency. Once we have f, we use Ohm's law (I(t) = V(t)/Z) with Z = R to find the steady-state current at resonance, noting that the voltage is an RMS value.