# 9.5: Procedure

## 9.5.1: RC Circuit

1. Using Figure 9.4.1 with a 10 V p-p 10 kHz source, R = 1 k$$\Omega$$, and C = 10 nF, determine the theoretical capacitive reactance and circuit impedance, and record the results in Table 9.6.1 (the experimental portion of this table will be filled out in step 6). Using the current divider rule, compute the resistor and capacitor currents and record them in Table 9.6.2.

2. Build the circuit of Figure 9.4.1 using R = 1 k$$\Omega$$, and C = 10 nF. A common method to measure current using the oscilloscope is to place a small current sense resistor in line with the current of interest. If the resistor is much smaller than the surrounding reactances it will have a minimal effect on the current. Because the voltage and current of the resistor are always in phase with each other, the relative phase of the current in question must be the same as that of the sensing resistor’s voltage. Each of the three circuit currents will be measured separately and with respect to the source in order to determine relative phase. To measure the total current, place a 10 $$\Omega$$ resistor between ground and the bottom connection of the parallel components. Set the generator to a 10 V p-p sine wave at 10 kHz. Make sure that the Bandwidth Limit of the oscilloscope is engaged for both channels. This will reduce the signal noise and make for more accurate readings. Also, consider using waveform averaging, particularly to clean up signals derived via the Math function.

3. Place probe one across the generator and probe two across the sense resistor. Measure the voltage across the sense resistor, calculate the corresponding total current via Ohm’s law and record in Table 9.6.2. Along with the magnitude, be sure to record the time deviation between the sense waveform and the input signal (from which the phase may be determined eventually).

4. Remove the main sense resistor and place one 10 $$\Omega$$ resistor between the capacitor and ground to serve as the capacitor current sense. Place a second 10 $$\Omega$$ resistor between the resistor and ground to sense the resistor current. Leave probe one at the generator and move probe two across the sense resistor in the resistor branch. Repeat the Ohm's law process to obtain its current, recording the magnitude and phase angle in Table 9.6.2. Finally, move probe two so that it is across the capacitor’s sense resistor. Measure and record the appropriate values in Table 9.6.2. Note that if you are using a four channel oscilloscope, simultaneous input, resistor and capacitor measurements are possible.

5. Move probe one to the resistor’s sense resistor and leave probe two at the capacitor’s sense resistor. Save a picture of the oscilloscope displaying the voltage waveforms representing $$i_R$$, $$i_C$$ and $$i_{in}$$ (i.e., the Math waveform computed from $$i_R + i_C$$).

6. Compute the deviations between the theoretical and experimental values of Table 9.6.2 and record the results in the final columns of Table 9.6.2. Based on the experimental values, determine the experimental Z and $$X_C$$ values via Ohm’s law ($$X_C = V_C/i_C, Z = V_{in}/i_{in})$$ and record back in Table 9.6.1 along with the deviations.

7. Create a phasor plot showing $$i_{in}$$, $$i_C$$, and $$i_R$$. Include both the time domain display from step 4 and the phasor plot with the technical report.

## 9.5.2: RL Circuit

8. Replace the capacitor with the 10 mH inductor (i.e. Figure 9.4.2), and repeat steps 1 through 7 in like manner, using Tables 9.6.3 and 9.6.4.

## 9.5.3: RLC Circuit

9. Using Figure 9.4.3 with both the 10 nF capacitor and 10 mH inductor (and a third sense resistor), repeat steps 1 through 7 in like manner, using Tables 9.6.5 and 9.6.6. Note that it will not be possible to see all four waveforms simultaneously in step 5 if a two channel oscilloscope is being used. For a four channel oscilloscope, place a probe across each of the three sense resistors.