The purpose of this lab was to gain understanding of the concept of impedance in resistors, capacitors and inductors. When AC current is applied to a circuit, these elements will exert a small amount of resistance due to the changing current/voltage of the AC input. Three different circuits were analyzed, one containing two resistors in series, one containing a resistor and inductor in series, and another containing a resistor and capacitor in series. The input voltage was a sinusoidal wave with amplitude 2 V and frequencies of 1000, 5000, and 10000 Hz were tested on each circuit.
In each circuit, R = 47 Ohms. The voltage across this resistor was recorded in each circuit and divided by 47 to determine the amplitude of the current in the circuit. All input and output voltages, and the function for the current, were recorded using the oscilloscope in the Waveforms program.
Actual values for each circuit element
Before starting the lab, a wall of math was created to determine the function for the current through each circuit for various input frequencies.
The first circuit tested was the one containing two resistors. This circuit contains one 47 Ohm resistor in series with a 100 Ohm resistor. The actual circuit, as well as the oscilloscope readings are pictured below.
1000 Hz
Current through the circuit in mA
5000 Hz
Current through the circuit in mA
10000 Hz
Current through the circuit in mA
According to our wall of math, the current across the 47 Ohm resistor should have been 13.4 mA; we obtained an actual current with an amplitude of 15 mA, which is very close to our prediction.
The second circuit tested contained the same 47 Ohm resistor in series with a 1 mH inductor. The actual circuit, as well as the recorded oscilloscope are pictured below.
1000 Hz
Blue = V_in , Yellow = V_out , Red = Current (mA)
5000 Hz
Blue = V_in , Yellow = V_out , Red = Current (mA)
10000 Hz
Blue = V_in , Yellow = V_out , Red = Current (mA)
According to the calculations in our wall of math, the amplitude of current should have been slightly less than 40 mA for each frequency, and the phase should shift slightly negative (to the right) as the frequency increased. The results shown above indicate that the phase slightly increases as the frequency increases, just as predicted. The actual currents turned out to be slightly off from what we predicted, but the trend that the current slightly decreases as frequency increases was still seen.
The final circuit analyzed contained the 47 Ohm resistor in series with a 47 micro Farad capacitor. The actual circuit, as well as the oscilloscope readings, are shown below.
1000 Hz
Blue = V_in , Yellow = V_out , Red = Current (mA)
5000 Hz
Blue = V_in , Yellow = V_out , Red = Current (mA)
10000 Hz
Blue = V_in , Yellow = V_out , Red = Current (mA)
According to our predictions, the amplitude of current should go from 1 mA at 1000 Hz to 4.6 mA at 5000 Hz and 9.1 mA at 10000 Hz. So, the amplitude scales by the same factor as the frequency of input voltage. Though the value of our amplitude of current does not match with the results shown in the oscilloscope, it can be seen that the current scales in the same manner as predicted. Also, the phase shift changes with the frequency just as we predicted. It goes from -89° at 1000 Hz to -84° at 5000 Hz, and to -77° at 10000 Hz. In other words, the phase starts out at ~ -90° and slowly shrinks down as the frequency increases, which brings the input and output voltages closer together on the oscilloscope readings.
In Class Examples
1. Find v(t) and i(t) for the circuit below:
2. Given that is(t) = 5 sin (1000t) A, find vc(t):
3. For the circuit below, find Zin for w = 1000 rad/s where the inductor is 20H
4. Determine vo(t) in the circuit shown.
5. What is the phase shift if R = C at a particular frequency?
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