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11-17-11 Sinusoidal Response of RC and RL Circuits

Eq 3 two ways to find phase shift either using

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Eq 3. Two ways to find phase shift, either using variables or measured values Eq 4. The equation to find output voltage
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Procedure I. RC Circuit For this portion of the lab, we were asked to build the circuit in Figure 1, a simple RC circuit. Of note is the additional 50Ω resistor, this is the internal resistance of the function generator. After calculating the values by hand, we built the circuit with a 320Hz, 10Vp-p, sine wave as the source voltage. Using the oscilloscope, we then measured the waves. Figure 1. The RC circuit for part 1. The additional resistor (R2) is the internal resistance of the function generator. Figure 2. The graph from the oscilloscope in the lab, at a frequency of approximately 3.2kHz Table 1. The values of the measured with the real oscilloscope. Frequency Input Voltage () Output Voltage () Output Voltage () V-I Time Difference () Phase Shift () Resistor Current () 320 Hz 10 V 0.352 V 0.124 V 720 μs 82.94 1.245 mA 3.2 kHz 10 V 2.04 V 0.674 V 64 μs 73.728 6.74 mA 32 kHz 10 V 8.32 V 2.85 V 3.2 μs 36.864 28.5 mA 320 kHz 10 V 9.40 V 3.10 V 80 ns 9.216 31.0 mA Table 2. The calculated values. Frequency Output Voltage () Output Voltage () V-I Time Difference () Phase Shift () Resistor Current () 320 Hz 0.1971 V 0.1393 V 766.2μs 88.27 1.393 mA 3.2 kHz 1.674 V 1.183 V 63.55μs 73.21 11.83 mA 32 kHz 6.678 V 4.722 V 1.592 μs 18.34 47.22 mA
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320 kHz 9.526 V 6.736 V 16.4 ns 1.899 67.36 mA As can be seen by comparing the two tables, our error grew as the frequency was pushed higher. This is due to the difficulty in making precise measurements with the oscilloscope and these levels.
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