Experimental study of the frequency repulsion effect
Inductively coupled LC circuits.
Inductively coupled RLC circuits. The resistance is the internal resistance of the AC source, and and are the internal resistances of inductors having inductances and , respectively. The voltage drop in the resistances of the primary and secondary circuits is measured directly by the lock-in amplifier. is the voltage drop in the resistance and is used to monitor the currents in each network.
Schematic of the experimental setup. The two coils move along a wooden rod. Here is the separation between the coils. An AC source is connected to the primary circuit.
Experimental results for the mutual inductance as a function of the separation . The diamond symbols are the results for obtained by direct measurements of . The continuous line is an empirical fit to the data using an exponential function.
The observed current amplitude in the primary circuit as a function of frequency for different separations between the coils. The frequency separation of the maxima of these curves increases for smaller distances, that is, stronger coupling.
The observed current amplitude in the secondary circuit as a function of frequency for different separations between the coils. As in Fig. 5, the frequency separation of the maxima increases for smaller distances.
The observed current amplitude as a function of the frequency in the primary (crosses) and secondary (circles) circuits for . The continuous lines are fits to the data using Eq. (A10) with the mutual induction coefficient as the only adjustable parameter. The values of obtained for each value of are shown in Fig. 4.
Observed maximum response frequencies as a function of . The heavy lines are the result of Eq. (10). The dotted horizontal lines indicate the uncoupled eigenfrequencies. The square symbols and triangles represent the eigenfrequencies (frequencies of the maxima in the secondary circuit of Fig. 6).
Values of the parameters used. The second column shows the values of the parameters obtained by direct measurements. The third column shows the results obtained from a fit of the data, as illustrated in Fig. 6. In this case the model provides only the total resistance of the circuit.
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