# LAB253 Troy University Resistance and Capacitance in A Circuit Analysis

Please answer all questions in the RC circuit document. include the question in Analysis part.

Resistance and capacitance in a circuit

When resistance and capacitor are connected in series, capacitor acts as a device for storing charge. The amount of charge stored is directly proportional to voltage applied, Q = CV. When battery in turned on, capacitor starts charging until it reaches to maximum voltage supplied by battery. Since capacitor is storing the charge so amount of current in the circuit keeps decreasing across the resistance. Once the capacitor is fully charged and disconnected from battery, it will discharge through the resistance. When the amount of charge stored in capacitor decreases, the amount of current through the resistance is also decreased. During charging and discharging of the capacitor, the current will decrease exponentially as the function of time. The time in which the current reduced to 1⁄2 of its maximum value is defined as half life. The half life can be calculated using the formula

τ1/2 =ln2RC

You will measure be two RC decay half-lives. The first will be long enough to measure using a multimeter and a stopwatch.Step 1

Set up the circuit below with the power supply off.

Step 2

Turn on the power supply, adjust it to 2-3 volts and start the stopwatch. Record the time and 5000Ω and 20000μF voltage every 15 seconds for 5 minutes.

Step 3

Disconnect the wires from the power supply and short them together. Again, record the time and voltage every 15 seconds for 5 minutes.

Step 4

Plot the data from step 1 and 2 on separate plots. Find an experimental half-life from both plots.

Step 5

Using that resistance and your measured half-life (from step #4) get an experimental value for capacitance of C which should match with theoretical value given on the capacitor( 0.2 F).

Setup

1. Construct the circuit shown in Figure 2. The voltage source is Signal Generator #1 on the 850 Universal Interface. C = 3900 pF and R = 47 kΩ.

Figure 2. RC Circuit Diagram

2. Click on Signal Generator #1 to connect the internal Output Voltage-Current Sensor. Set the signal generator to a 350 Hz square wave with 2 V amplitude and 2 V offset. This will make the square wave all positive with an amplitude of 4 V. Set the signal generator on Auto.

3. Plug the Voltage Sensor into Channel A. Connect the Voltage Sensor across the capacitor.

Procedure

1. Set up an oscilloscope display with the Voltage Ch.A and the Output Voltage on the same axis. Click Monitor and adjust the scale on the oscilloscope so there is a complete cycle, so the capacitor fully charges and discharges.

2. Increase the number of points (using the tool on the scope toolbar) to the maximum allowed. Then take a snapshot of both voltages shown. Rename the snapshots “3900pF”.

Analysis

1. Create a graph with Voltage Ch.A and the Output Voltage vs. time. Select the voltages for the 3900 pF run on the graph.

2. Using the Coordinates Tool, measure the time it takes for the voltage to decay to half of its maximum. This time is the half-life. It may be necessary to reduce the snap-to-pixel distance to 1 in the properties of the Coordinates Tool (right click on the tool to access the properties).

3. Measure the time it takes for the voltage to decay to one-quarter of its maximum. This is two half-lives. Then divide this time by two to find the half-life.

4. Measure the time it takes for the voltage to decay to one-eighth of its maximum. This is three half-lives. Then divide this time by three to find the half-life. Take the average of the three measured values of the half-life. Estimate the precision of the measurement and state it as {half-life ± precision}.

5. Calculate the theoretical half-life given by Equation (12) and compare it to the measured value using a percent difference.

Conclusions

1. Summarize how changing the voltage and capacitance changes the half-life.

2. Include the values found for the half-lives and the % differences. Does the theoretical value lie within the range of precision of your measurements? Explain what causes the differences.

3. Did your answers to the Pre-Lab Questions agree with the results?

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