Frequency Dependence of Impedance

We wish to measure the magnitudes of the impedances and by measuring and V which will be proportional to the impedances if is kept constant. However, as the frequency of the signal generator is varied, not only does the impedance of L and C change, but the impedance of the whole circuit changes. Hence, if V (the amplitude of the signal generator's output) is left constant when the frequency is changed, will therefore change. To keep constant, we need to adjust so that the voltage across the resistor R remains constant.

Use the oscilloscope to measure the voltage drop first across L and then across C for a wide range of frequencies, measuring between each change of frequency and adjusting to keep (and therefore ) constant.

 

Figure 9.7: Measuring or .

To measure , the circuit must be reconnected so that the signal generator and the oscilloscope share a common ground.

 

Figure 9.8: Measuring .

You should check the frequency settings of the signal generator by measuring the periods of oscillation with the oscilloscope.

Plot the results (choosing variables for ordinate and abscissa with some forethought) so as to make a simple graphical comparison with the equations for and . Note that if y=kx, then the graph of y vs. x should be a straight line. If y=k/x, then the graph of y vs. 1/x should be a straight line. What values of L and C are implied by your graphs?

In practice, the elements may not be pure R, L and C. The resistor may have some associated inductance, the inductance may have an appreciable resistance, etc. Do your curves show any evidence of these effects (do they show any systematic deviations from the expected behaviour)? Is there any danger that connecting the oscilloscope will alter the behaviour of the circuit (the 'scope has an input resistance of 1 M , with an input capacitance, in parallel, of 35 pF)?