26 Parallel RC Circuits OBJECTIVES: 1. 2. After performing this experiment, you will be able to: Measure the current pha

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26 Parallel RC Circuits OBJECTIVES: 1. 2. After performing this experiment, you will be able to: Measure the current phasors for a parallel RC circuit. Explain how the current phasors and phase angle are affected by a change in frequency for parallel RC circuits. READING: Floyd and Buchla, Principles of Electric Circuits, Sections 15-5 and 15-6 MATERIALS NEEDED: One 100 k resistor Two 1.0 k resistors One 1000 pF capacitor Application Problem: One 10 kn potentiometer, one 100 kA resistor, one 0.1 uF capacitor SUMMARY OF THEORY: In a series circuit, the same current is in all components. For this reason, current is used as a reference. In addition, Kirchhoff's voltage law applies to reactive circuits provided the voltages are added as phasors. By contrast, in parallel, the same voltage is across all components. The voltage is, therefore, the reference. Current in each branch is compared to the circuit voltage. In parallel circuits, Kirchhoff's current law applies to any junction. Current entering a junction must be equal to current leaving the junction. Again, care must be taken to add the currents as phasors. Figure 26-1 illustrates a parallel RC circuit. If the impedance of each branch is known, the current in that branch can be determined directly from Ohm's law. The current phasor diagram can then be constructed directly. The total current can be found as the phasor sum of the currents in each branch. The current in the capacitor is shown at +90" from the voltage reference because the current leads the voltage in a capacitor. The current in the resistor is along the x-axis because current and voltage are in phase in a resistor. The Pythagorean theorem can be applied to the current phasors, resulting in the equation += 4, +1, 2 tan" . 5.0 mA - 5.0mA Xc25 40 mA R133in 4-3.0mA Direction of voltage Creference) 30 mA (b) Current pesos (aCool Figure 26-1 247
2 drop that can be measured. These resistors are much smaller than the parallel branch impedance, so their resistance can be ignored in the computation of circuit impedance PROCEDURE: 1. Measure a resistor with a color-coded value of 100k and each of two current sense resistors Use the listed value if a measurement cannot be made. Record the measured values in Table 26-1. (Rs and Ro) with color-coded values of 100 Measure the capacitance of a 1000 pF capacitor. 2. Construct the circuit shown in Figure 26-2. Because you will be measuring some very small voltages in this experiment, use a voltmeter and record all voltages and currents as mms values Set the generator to a voltage of 3.0 V. at 10 kHz. Check both the voltage and frequency with your oscilloscope. (Note that 3.0 V._ is approximately 85 V.) w 10 WW 10 act 100 10 LO V-30V. Since Figure 26-2 3. Using the voltmeter, measure the rms voltage drop across each resistor. The voltage drops across the sense resistors are particularly small, so measure them as accurately as possible, keeping three significant figures in your answer. Record the voltage drops in Table 26-1. 4. Compute the rms current in cach resistor using Ohm's law. Record the computed current in Table 26-1. S. Draw the current phasors Ix and la and the total currently on Plot 26-1. The total current is in sense resistor Rs. The current la is in sense resistor Re. Ignore the small effect of the sense resistors on the phasor diagram. Note carefully the direction of the phasors. Label each of the current phasors. 6. Compute Xc for the 10 kHz frequency. Using this value and the measured resistance of Ri. compute the total impedance of the circuit using the product-over-sum rule for parallel resistance and reactance. The sense resistors can be ignored for this calculation, but you will need to use phasor math to obtain the correct result. Recced the values of Xa and Zy in the space provided in the report. The product-over-sum rule for this case is 2- RX-XXL) R-Xes 248
Using the Zy found in step 6 and the applied voltage, Vs.compute the total currently. Check that the total current agrees within experimental error with the value determined in step 4. Record the computed current in the space provided in the repon. Change the frequency of the generator to 2.0 kHz. Check that generator voltage is still 30V Repeat steps 1-5 for the 20 kHz frequency. Verify all measurements with the oscilloscope. Enter the data in Table 26-2 and draw the current phasors on Plot 26-2 POR FURTHER INVESTIGATION: bageries RC circuit, the impedance phasor is the vector sum of the resistance and reactance phasors. In a placuit, the admittance phasor is the vector sum of the conductance and the susceptance phasors. De Plor 26-3. draw the admittance, conductance, and susceptance phasors for the experimentat a Autor diagram by dividing the current phasors by the applied voltage.) way of 1.0 KHz. (Hint: The admittance phasor diagram can be obtained directly from the current UPPLICATION PROBLEM: Sine-control circuits can be used to limit the band of frequencies in an audio system. The tone control edit shown in Figure 26-3 uses both series and parallel RC circuits to provide high- and low-frequency estion. Construct the circuit. Connect one channel of your oscilloscope across the input signal generator and the other channel across the load resistor and view the signals together. Start by setting the stal generator to 1 Vpat 100 Hz. Which control affects the low-frequency response? Try setting the generator to 1 kHz and then to 10 kHz. Test the effect of each control on the response. Explain the circuit and your measurements in your report. 10 w RA 와 Los 1000 pl Function generator 10V pp Sinewave Figure 26-3 De accurate absolute voltages. Relative voltages will allow impedances to be correctly determined Most DMMs can measure the relative voltages at this frequency: however, some DMMs will not 249
Report for Experiment 26 Name Date Class ABSTRACT: DATA: Computed Current Table 26-1-1.0 kHz) Listed Measured Voltage Value Value Drop R 100 ΚΩ R 1.0 KN Re 1.02 1000 pF 9 Z Plot 26-1 Xa Iy Table 26-2 (1-2,0 kHz) Listed Measured Voltage Value Drop Computed Current Value R 100 kΩ R10 kn R 1.00 4 1000 pF Plot 262 Z=- Xc - - I= -
LATION AND REVIEW QUESTIONS: Explain how increasing the frequency affects cach of the following the total impedance of the circuit (a) the phase angle between the generator voltage and the generator current (6) (a) (5) (c) Assume the frequency had been set to 5.0 kHz in this experiment. Compute: the current in the resistor the current in the capacitor the total current If a smaller capacitor had been substituted in the experiment, what would happen to the current phasor diagrams? A common circuit using a parallel RC circuit is the bypass capacitor across the emitter resistor in a transistor amplifier, as illustrated in Figure 26-4. The frequency at which the resistance Re is equal to the capacitive reactance Xc is called the cutoff frequency Compute the cutoff frequency for the circuit by setting Re = Xc and solving for f. R C 10 MF (b) b) How do the branch currents compare at the cutoff frequency? Figure 264 (c) Explain what happens above this frequency to the current in the parallel RC circuit. If the capacitance in Figure 26 4 is increased, what happens to the cutoff frequency? What is the phase angle between the source voltage and current at the cutoff frequency?