Experiment Report: Measuring Time Constants in RL and RC Circuits, Lab Reports of Electronics

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Carlyn Annunziata EENG 275 Experiment 5: Frequency domain and time domain Harminder and Sara Professor Islam 11/12/

Objective: An electric current, flowing through a wire conductor results in a magnetic flux developing around the conductor. At the same time, an electromotive force (voltage) is induced within the coil in the direction which reduces fluctuation of the current. An inductor is a passive electrical component which is capable of storing the electrical energy as a form of magnetic energy. The voltage across an inductor can be determined using Kirchhoff’s voltage law, where Vs = VR + VL, and VS is the source voltage and VR and VL represent the voltage across a resistor and inductor, respectively. At the initial time, where t=0, the inductor behaves as an open circuit, and no current is assumed to flow. After a time, t→ ∞, the inductor behaves as a short circuit. The time constant 𝜏𝐿, for the RL circuit is equal to R/L. At a time equal to the time constant, the current through the circuit is equal to 0.63 of the source voltage across the resistor. A capacitor, also a passive element, stores electrical energy in an electrical field. Kirchhoff’s voltage law is again utilized, and the voltage across a capacitor is represented as Vs = VR + VC. At initial time, the capacitor behaves as a short circuit, and after sufficiently long period of time, it behaves as an open circuit. The time constant for an RC circuit is 𝜏𝐶 = 𝑅𝐶. At a time equal to 𝜏𝐶, the current is equal to. of the source voltage across the resistor. The following lab report describes the use of a function generator and oscilloscope as a means to measure the time constants rise time for RL and RC circuits. The values obtained for the time constants are verified by comparison to calculated values. Additionally, the transient characteristics of electricity in RL and RC circuits are analyzed. Materials 1 - NYIT supplied Lab Kit 1 - Function Generator 1 - Oscilloscope 1 - Digital Multi-meter (DMM) 1 - DC Power Supply 1 - 51 Ω Resistor 1 - 220 Ω Resistor, 1 - 3 k Ω Resistor 1 - 0.01 μF Capacitor 1 - 10mH Inductor

𝑅 𝐿

The circuit in figure 5.1 was constructed ( image not shown), and the Function generator was set to produce a square wave from 0-5Vp and a frequency of 3kHz. Using equation 1, the value for the rise time is determined using algebraic manipulation. Figure 2 depicts the experimentally derived wave form of the circuit shown in Figure 5.11. The value for 𝜏𝐶 is determined from equation 2. From figure 2, the resultant waveform using the function generator parameters outlined is demonstrated to be a “rippled” waveform, which is normally observed in RC circuits, and is consistent with the expected waveform shown in the lab notes provided by the instructor. In Figure 3, the time constant 𝜏𝐶, was determined experimentally by setting the cursor type to “voltage” and using the vertical position knobs the point which the capacitor was fully charged and discharged was marked with horizontal lines (cursors) on the waveform. Next, the cursor was set to type “time” and the delta value obtained from the previous step was marked with one of the vertical cursors and the fully charged point was marked with the second vertical cursor. The delta value indicates the time constant 𝜏𝐶. Figure 2: Figure 3:

Figure 5.12: For the RL circuit, depicted in Figure 5.12, the rise time is found using equation 3, and the time constant is obtained from equation 4. Figure 3 shows the waveform obtained from the simualted results of the circuit depicted in Figure 5.12, and Figure 4 shows the waveform obtained from the experimental set up. Both of these waveforms shown in Figure 3 is consistent with the expected waveform, which was depicted in the lecture notes provided by the instructor. In Figure 5 , the time constant 𝜏𝐿, was determined experimentally by setting the cursor type to “voltage” and using the vertical position knobs the point which the inductor carried the most electrical energy and least electrical energy was marked with horizontal lines (cursors) on the waveform. Next, the cursor was set to type “time” and the delta value obtained from the previous step was marked with one of the vertical cursors and the point of maximal electric energy in the inductor was marked with the second vertical cursor. The delta value indicates the time constant 𝜏𝐿.