Final answer:
The question is about determining the value of input resistance (rin) at mid-frequency in ohms for an RLC series circuit, but the required specific information for the calculation is not provided. Instead, the response explains the method of calculating impedance, which is related to how resistance would be considered within the circuit for a given frequency.
Step-by-step explanation:
The student has asked to determine the value of the input resistance, usually denoted as rin, at mid-frequency in ohms for an RLC series circuit. However, based on the provided context, it seems there's a lack of specific information needed to calculate rin directly. Normally, rin could refer to the total resistance at resonance, or it could be about finding the parallel resistance in certain configurations. To calculate something like a resonant frequency input resistance (rin), one would need to know the values of the various components and the specific setup of the circuit being analyzed.
Since the question does not provide enough details to calculate rin for the specific mentioned examples, I will instead clarify how impedance is calculated, as impedance includes resistive effects at a particular frequency. The formula to find the impedance in an RLC circuit at a particular frequency is Z = √(R² + (XL - XC)²) where R is resistance, XL is inductive reactance (XL = 2πfL), and XC is capacitive reactance (XC = 1 / (2πfC)). To calculate the impedance and current (Irms) at specific frequencies, you need to use the values of R, L, C and the given frequency to find XL and XC first and then apply the mentioned formula.