Derive a formula for the rms-amplitude of the current I_1 in the primary circuit expressed with known and/or measured quantities (give the equation)!

What is the I_rms?

Determine the resonance frequency f_0! You can make a fit with a suitable model, interpolate smartly between data points, or read off with an eye, but you MUST give a qualified estimate of the uncertainty in f_0.

Based on your result for the resonance frequency, determine the inductance L_1 of the primary coil and its uncertainty!

Provide an equation that allows determining R_L based on the rms-amplitude I_1(f_0) of the primary current at resonance!

Determine a value for R_L and its uncertainty!

Make a plot of the ratio between secondary voltage U_B and primary current I_1 as a function of frequency. Make a fit with a suitable model function!

Determine a value for the mutual inductance M_12 and its uncertainty!

How large must the inductance L_2 of the secondary coil be at least? Use the inequality: (M_12)^2 < L_1 * L_2 What happens to the mutual inductance if the input voltage U_SG is doubled in a new measurement?

The following is the description: An RCL series circuit, as shown in Fig.1, is driven by an ideal AC voltage source . The source delivers a sinusoidal voltage with the rms amplitude U_SG = (114.5 0.1) mV_rms and frequency f. The source has a built-in resistance (output impedance) of R_SG = 50. The components in the resonance circuit are a coil with inductance L_1 and series resistance R_L, a capacitor C = 47nF, and a damping resistor R = 39.1. The coil L_1 is connected to a secondary coil L_2 via the mutual inductance M_12. The uncertainties in all given component values and in the frequency are assumed to be vanishingly small. Voltage drops U_A over R and C are measured in the primary circuit, and the induced voltage U_B over the coil L_2 in the secondary circuit. The input impedance of the measuring instruments is assumed to be infinitely high, i.e., we can ignore the current through the measuring instruments. The data file DataHandIn1_2022.txt contains measured rms voltages U_A and U_B and their uncertainties dU_A and dU_B for 17 different values of the frequency

Figure 1: Circuit diagram of the setup with RCL series circuit as primary circuit and coil L_2 in the secondary circuit.