Final answer:
The inductance of the solenoid can be calculated from the slope of the graph plotting the square of the resonant angular frequency (ωres2) against the inverse of capacitance (1/C), while the resistance of the solenoid is computed using Ohm's Law, with known maximum current and voltage amplitude.
Step-by-step explanation:
The question relates to an RLC series circuit in an AC context and involves finding the inductance and resistance of a solenoid when a capacitor and AC source are in series with it. Given the relationship between the square of the resonant angular frequency (ωres2) and the inverse of capacitance (1/C), and the fact that maximum current is achieved at resonant frequency, we can employ the formula ωres2 = 1 / (LC) to determine the inductance (L) of the solenoid. Furthermore, the resistance (R) can also be computed knowing that at resonance, the impedance is purely resistive (Z=R), and using Ohm's Law (V=IR), the resistance can be calculated as R = V / Imax, where V is the voltage amplitude and Imax is the maximum current.
To calculate inductance (L), one would use the slope of the graph of ωres2 versus 1/C, since the slope equals 1/L. For resistance (R), given the maximum current is 2.50 A and the voltage amplitude is 90.0 V, the resistance would be R = 90.0 V / 2.50 A. This application of circuit analysis and resonance in an RLC circuit is a common topic in electrical engineering and physics courses, providing essential principles for understanding AC circuits and their behavior at different frequencies.