DE LA SALLE LIPA COLLEGE OF INFORMATION TECHNOLOGY AND ENGINEERING ELECTRICAL ENGINEERING DEPARTMENT CKTS002 – CIRCUITS 2 LABORATORY EXPERIMENT MANUAL EXPERIMENT #1: SERIES RC AND RL CIRCUITS I. OBJECTIVES 1. To analyze the phasor relationships of voltage and current for RC circuit. 2. To analyze the phasor relationships of voltage and current for RL circuit. II. DISCUSSION Ohm’s law applies to all types of circuits, but in the case of AC circuits all currents, voltages, reactances, resistances, and impedances must be expressed as phasors. All calculations must be done vectorially with reference to a phasor diagram. All phasor diagrams should be accompanied by a circuit diagram. If this is not done, then such a circuit diagram must be obvious or assumed in order to interpret the phasor diagram. The phasor diagram shows only the magnitude and relative phase angles of the currents and voltages while the circuit diagram shows only the location, direction and polarity of the currents and voltages. These are important distinctions and confusion generally results when not recognized or when the two diagrams are combined. The circuit diagram of a series RC circuit is shown in Fig. 1.1a. The current through a capacitor leads the voltage across it by 90 degrees. Since the same current flows through the capacitor as flows through the resistor and since the voltage across the resistors in phase with the current through it, we may conclude that the voltage across the resistor leads the voltage across the capacitor by 90 degrees. This relationship is shown as the phasor diagram in Fig. 2.1b. From the phasor diagram, ET = ER – jEC. We observe that from Ohm’s law, we have: ET = IZ, ER = IR and EC = IXc. From these equations, we can compute the impedance of a series RC circuit. The impedance is given by the equation, Z = R - jXC. Xc can be computed if frequency and capacitance are known by the equation Xc = ½ π f C. The circuit diagram of a series RL circuit is shown in Fig. 1.2a. The current through the inductor lags the voltage across it by 90 degrees. Since the same current flows through both elements, the voltage across the resistor lags that across the inductor by 90 degrees. The phasor diagram showing these voltages is given below. From the phasor diagram, we have: E T = ER + jEL. We know from Ohm’s law that ET = IZ, ER = IR and EL = IXL. From which the total impedance of the series RL circuit is given by Z = R + jXL. If frequency and inductance are known, we could compute for XL using the equation XL= 2 π f L. 1 DE LA SALLE LIPA COLLEGE OF INFORMATION TECHNOLOGY AND ENGINEERING ELECTRICAL ENGINEERING DEPARTMENT CKTS002 – CIRCUITS 2 LABORATORY EXPERIMENT MANUAL (a) circuit diagram (b) phasor diagram Fig. 1.1 Series RC circuit (b) circuit diagram (b) phasor diagram Fig. 1.2 Series RL circuit III. COMPONENTS NEEDED ITEM NO. IV. DESCRIPTION AC voltmeter AC ammeter Lamp (10 Ω) 50 H inductor 0.15 F capacitor 12V AC Power Supply PROCEDURE RC circuit: 1. Connect the circuit shown in Fig. 1.3. 2. Set the AC power supply to 12V, 0.1 Hz. 3. Record the current I and voltages ER and EC. 2 QUANTITY 1 1 1 1 1 1 DE LA SALLE LIPA COLLEGE OF INFORMATION TECHNOLOGY AND ENGINEERING ELECTRICAL ENGINEERING DEPARTMENT CKTS002 – CIRCUITS 2 LABORATORY EXPERIMENT MANUAL 4. Using Ohm’s law, compute the magnitude of the impedance network. Record it as the measured value. 5. Compute the magnitude and phase angle of the impedance using the equation Z = R - jXC where XC = 1/ 2 π fC. 6. Compute the percentage difference between the measured and compared value of the impedance. RL circuit: 1. 2. 3. 4. Connect the circuit shown in Fig. 1.4. Set the AC power supply to 12V, 0.1 Hz. Record the current I and voltages ER and EL. Using Ohm’s law, compute the magnitude of the impedance network. Record it as the measured value. 5. Compute the magnitude and phase angle of the impedance using the equation Z = R + jXL where XL = 2 π fL. 6. Compute the percentage difference between the measured and compared value of the impedance. V. CIRCUIT DIAGRAM Fig 1.3. Capacitive circuit Fig 1.4. Inductive circuit VI. DATA AND RESULTS CIRCUIT ET I ER EC Series RC Series RL 3 EL Z (meas) Z (comp) % diff Ɵ (comp) DE LA SALLE LIPA COLLEGE OF INFORMATION TECHNOLOGY AND ENGINEERING ELECTRICAL ENGINEERING DEPARTMENT CKTS002 – CIRCUITS 2 LABORATORY EXPERIMENT MANUAL VII. QUESTIONS 1. A circuit contains a fixed resistor in series with variable capacitor. Plot the curve to show the variation of the impedance with capacitive reactance as the capacitance is varies from zero to an infinitely large value. 2. A pure capacitor and pure resistor are connected in series in an AC circuit. A voltmeter reads 30 V when connected across the capacitor and 40 V when connected across the resistor. What will it read when connected across both? 3. A current of 25 A is observed in 120 V 60 Hz circuit which consist of a pure resistor and a pure inductor in series. The voltages across the resistor and inductor are found to be identical. Calculate the value of the resistance and the inductance. VIII. CONCLUSION References: Electrical Engineering Department: Laboratory Experiment Manual - Electrical Circuits 2 Online Resources: https://phet.colorado.edu/sims/html/circuit-construction-kit-ac/latest/circuit-constructionkit-ac_en.html 4