Series connection of capacitors

Theory:

Capacitors follow the same law using the reciprocals. The total capacitance of capacitors in series is equal to the reciprocal of the sum of the reciprocals of their individual capacitances:

.

Experimental part:

Figure 3.1

· Collect the circuit on the Figure 3.1 with sinusoid Voltage Vm=5 V, f=2 kHz.

· Transfer data from A1 and V0 (virtual devices) to the Table 3.1

Table 3.1

I, mА	U,B
77.0	4.8	2.91	1.3	0.6

 

· A rating of capacitive reactance and capacity. Check the equivalent capacitance of the circuit calculation. The calculation of capacitive reactance:

 

376.6 Ohm 168.8 Ohm

77.9 Ohm 623.3 Ohm

Calculate w: = 12.56 kHz

0.2114 uF 0.4717 uF

1.022 uF 0.1277 uF

Checking the equivalent capacitance circuit calculation:

à à C_eq= 0.1303 uF

4. Parallel connection of capacitors:

Theory:

The total capacitance of capacitors in parallel is equal to the sum of their individual capacitances:

.

The working voltage of a parallel combination of capacitors is always limited by the smallest working voltage of an individual capacitor.

Experimental part:

Fig 4.1

· Collect the circuit on the Figure 4.1 with sinusoid Voltage Vm=5 V, f=1 kHz.

· Transfer data from A1 and V0 (virtual devices) to the Table 4.1

Table 4.1

	I, mА	mА	, mА	, mА
4.9	53.0	6.9	14.7	31.4

· Calculate and compare with practical value:

723.3 Ohm 341.1 Ohm

160.1 Ohm 924.5 Ohm

Measured: Calculated:

C_eq = 1/(w*X_eq) = 1.722 uF C_eq=(1.0+0.22+0.47)uF= 1.69 uF

 

Conclusion:

In this lab work we learned about alternating current circuit with capacitor. We found that in direct current (DC) circuits after the initial charge or discharge no current can flow, in AC circuits current flows all the time into and out of the capacitor, depending on the impedance in the circuit.

By the 1^st task we found that current through capacitor leads voltage by a quarter phase or 90 degrees. We had some errors in measurements, because had the instrumental errors and couldn’t find exactly points (which should write) on the graph.

In the 2^nd experiment we should determine reactive resistance of the circuit. According to the measurements we plot the graph and found that impedance in this circuit is reactive resistance of capacitor, which depends on the frequency of source and capacitance of capacitor.

3^rd and 4^th experiments are about series and parallel connections of capacitors, we learned about relation between equivalent capacitance and equivalent impedance of circuit. We also had some errors in measurements, it depends for devices errors.