VARIATION OF CAPACITIVE REACTANCE WITH CAPACITANCE

To find the variation of capacitive reactance with capacitance, we have conducted three experiments in order to get the variation graph, and the result.

Experiment 1:To determine if capacitors work with AC or DC current.

Equipments used:

1. Phillips Bulb (3.5V, 0.3A)
2. 9V Panasonic battery
3. AC source (signal generator: Instek GFG-8020H, stated generator ±1%)
4. Capacitor
5. Wire and a breadboard

Procedure:

First a circuit was setup as shown in figure 1.1 with the DC source, capacitor and battery all connected in series and any changes in the working of the bulb were noted.

Figure 1.1:  Circuit connected to a DC supply

Next, a circuit was setup as shown in figure 1.2 with the AC source replacing the DC source, and any change in the working of the bulb was noted.

Figure 1.2: Circuit connected to an AC supply

Result:

    Table1 below shows the observations made when a dc and ac voltage were introduced into Figures 1.1 and 1.2.

    Table 1: Observations of AC and DC inputs

Experiment 2:Variation of Capacitive Reactance with Capacitance.

Equipments used:

1. DIGIAC 3000 board, accuracy unknown
2. Digital multi-meter: ProsKit 3PK-600T, stated accuracy ±0.8%
3. Signal generator: Instek GFG-8020H, stated generator ±1%
4. Oscilloscope: Instek GOS 3PK-622G, stated accuracy ±3%

Procedure:

The oscilloscope was set as follows: Time base = 0.2ms/division.,AC triggers, Dual trace operation. CH1 vertical gain = 2V/division AC input. CH2 vertical gain = 50mV/division AC input.

Figure 2.1: Schematic of circuit to measure the voltage across the capacitor.

The schematic of the circuit constructed is as shown in figure 2.1 above. A signal generator, a resistor and a 47nF capacitor were all connected in series with the supply lines. The signal generator was set to sinusoidal waveform, frequency = 500Hz and output = 12V peak to peak. The two channels of the oscilloscope were connected across the capacitor. With the multi-meter set to 20V AC range, the voltage across the capacitor was measured and recorded.

The multi-meter was disconnected and set as an ammeter. It was then connected in series as shown in figure 2.2 below to measure the current flowing in the 47nF capacitor.

Figure 2.2: Schematic of circuit to measure the current through the capacitor.

By replacing the 47nF capacitor with a 100nF, 220nF and 470nF capacitor one a time; corresponding values of current were measured and recorded. The corresponding reactance Xc, were then calculated for the different capacitances and the results tabulated.

Result:

Table 2 below shows the experimental values obtained for the voltage, current and capacitive reactance at different capacitance values. The capacitive reactance (Xc) was calculated using the formula Xc = V / I [3]. The voltmeter readings were assumed to be the same for all the frequency values.

 Table 2: Different capacitance yields different capacitive reactance values

Figure 4 below is a scatter graph with a curve of best fit of capacitive reactance versus capacitance. It depicts the variation of capacitive reactance and capacitance. The values of the points plotted were obtained from Table 2.

Discrepancies:

Table 3 below show the discrepancies between the experimental values and actual values (values that should have been on the curve). The formula used to calculate the discrepancy (in percentage) is:

 % discrepancy = (Actual value – Experimental value) x 100

                                                Actual value

Table 3: Percent discrepancy between the actual and experimental values

Experiment 3:  Pure capacitance on an AC supply.

Equipments used:

1. DIGIAC 3000 board, accuracy unknown
2. Digital multi-meter: ProsKit 3PK-600T, stated accuracy ±0.8%
3. Signal generator: Instek GFG-8020H, stated generator ±1%
4. Oscilloscope: Instek GOS 3PK-622G, stated accuracy ±3%

Procedure:

The set up of this experiment was very similar to the previous experiment. The oscilloscope was set as follows: Time base = 0.2ms/division.,AC triggers, Dual trace operation. CH1 vertical gain = 2V/division AC input. CH2 vertical gain = 50mV/division AC input.

Figure 3.1: Circuit to measure the voltage across the capacitor.

The schematic of the circuit constructed is as shown in figure 2.1 above. A signal generator, a resistor and a 100nF capacitor were all connected in series with the supply lines. The signal generator was set to sinusoidal waveform, frequency = 500Hz and output = 12V peak to peak. The two channels of the oscilloscope were connected across the capacitor.

With the multi-meter set to 20V AC range, the voltage across the capacitor was measured and recorded.

 The multi-meter was then disconnected and set as an ammeter. It was then connected in series as shown in figure 3.2 below to measure the current flowing in the 100nF     capacitor.

Figure 3.2: Circuit to measure the current through the capacitor.

By changing the frequency from the signal generator to 1KHz, 2KHz and 4KHz one at a time, the corresponding values of current were measured and recorded. . The corresponding reactance Xc, were then calculated for the different frequencies and the results tabulated.

Result:

Table 3 shows the experimental values obtained for the voltage, current and capacitive reactance at different frequencies. The capacitive reactance was calculated using the formula Xc = V / I. The voltmeter readings were assumed to be the same for all the frequency values.

Table 4: Different frequencies of the input signal yield different capacitive reactance values

 Figure 5 below illustrates a curve of best fit of capacitive reactance versus frequency. The points plotted on the graph were obtained from Table 3.

Discrepancies:

Table 4 below show the discrepancies between the experimental values and actual values (values that should have been on the curve). The formula used to calculate the discrepancy (in percentage) is:

% discrepancy = (Actual value – Experimental value) x 100

                                                Actual value

Table 5: Percent discrepancy between the actual and experimental values