# Electricity & Electronics 8: Capacitors in Circuits

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1 Electricity & Electronics 8: Capacitors in Circuits Capacitors in Circuits IM This unit considers, in more detail, the charging and discharging of capacitors. It then investigates how capacitors behave in ac circuits and describes some of their uses. OBJECTIVES On completing this unit you should be able to: sketch graphs of current vs time and of voltage vs time for the charge and discharge of a capacitor in a dc circuit containing a resistor and capacitor in series. carry out calculations involving voltage and current in CR circuits using basic circuit rules (V = IR and V s = V 1 + V 2 ). state the relationship between current and frequency in a capacitive circuit. describe the principles of a method to show how the current varies with frequency in a capacitive circuit. describe and explain the function of a capacitor blocking dc while passing ac. Strathaven cademy Electricity and Electronics

2 CTIVITY 11 Title: Charging and Discharging Characteristics for a Capacitor im: To observe the variation of the current through, and the p.d. across, a capacitor during the charge and discharge cycles. pparatus 2200 µf capacitor, 10 kω resistor, ammeter and voltmeter, 6 V battery stopclock V - + Instructions Part 1: Charging Set up the circuit as shown with the switch open. The two meters will be replaced by connections to a computer interface. Close the switch and start the stopclock. Record values of current I and p.d. V every 10 seconds until the measured p.d. becomes constant. Plot graphs of current I and p.d. V against time for the charging cycle. Describe the change in the current and p.d. during the charging cycle. Part 2: Discharging j o i n l e a d s V - + Fully charge the capacitor as in Part 1. Disconnect the leads from the battery and join them together, as shown above. The two meters will be replaced by connections to a computer interface. Close the switch and note values for current I and p.d. V for the capacitor every 10 seconds from time t = 0. Plot graphs of current I and p.d. V against time for the discharge cycle. Explain the change in current and p.d. during the discharging cycle. Compare the direction of current during the charging and discharging cycles and explain any differences. Capacitance in a d.c. Circuit Strathaven cademy Electricity and Electronics

3 Charging Consider the following circuit:- When the switch is closed the current flowing in the circuit and the voltage across the capacitor behave as shown in the graphs below. current p.d. across capacitor Supply voltage 0 time 0 time Consider the circuit at three different times s soon as the switch is closed there is no charge on the capacitor the current is limited only by the resistance in the circuit and can be found using Ohm s law. s the capacitor charges a p.d. develops across the plates which opposes the p.d. of the cell as a result the supply current decreases. The capacitor becomes fully charged and the p.d. across the plates is equal and opposite to that across the cell and the charging current becomes zero. Strathaven cademy Electricity and Electronics

4 Discharging Consider this circuit when the capacitor is fully charged, switch to position B Capacitors in Circuits If the cell is taken out of the circuit and the switch is set to, the capacitor will discharge B B While the capacitor is discharging the current flowing in the circuit and the voltage across the capacitor behaves as shown in the graphs below. Current p.d. across capacitor Supply voltage 0 0 time time lthough the current/time graph has the same shape as that during charging the currents in each case are flowing in opposite directions. The discharging current decreases because the p.d. across the plates decreases as charge leaves them. Factors affecting the rate of charge/discharge of a capacitor When a capacitor is charged to a given voltage the time taken depends on the value of the capacitor. The larger the capacitor the longer the charging time, since a larger capacitor requires more charge to raise it to the same p.d. as a smaller capacitor as V= Q C When a capacitor is charged to a given voltage the time taken depends on the value of the resistance in the circuit. The larger the resistance the smaller the initial charging current, hence the longer it takes to charge the capacitor as Q = It (The area under this I/t graph = charge. Both curves will have the same area since Q is the same for both.) C u r r e n t C u r r e n t l a r g e c a p a c i t o r s m a l l c a p a c i t o r T i m e s m a l l r e s i s t o r l a r g e r e s i s t o r T i m e Strathaven cademy Electricity and Electronics

5 Example The switch in the following circuit is closed at time t = V 1 M V s 1 µ F Immediately after closing the switch what is: (a) the charge on C (b) the p.d. across C (c) the p.d. across R (d) the current through R. When the capacitor is fully charged what is: (e) the p.d. across the capacitor (f) the charge stored. (a) Initial charge on capacitor is zero. (b) Initial p.d. is zero since charge is zero. (c) p.d. is 10 V = V s - V c = 10-0 = 10 V (d) I R = V = = 10 (e) Final p.d. across the capacitor equals the supply voltage = 10 V. (f) Q = CV = = C. Strathaven cademy Electricity and Electronics

6 Frequency response of capacitor The following circuit is used to investigate the relationship between current and frequency in a capacitive circuit. S i g n a l g e n e r a t o r ( c o n s t a n t e. m. f. ) C u r r e n t ( ) 0 f r e q u e n c y ( H z ) The results show that the current is directly proportional to the frequency of the supply. To understand the relationship between the current and frequency consider the two halves of the a.c. cycle. Electrons Electrons The electrons move back and forth around the circuit passing through the lamp and charging the capacitor one way and then the other (the electrons do not pass through the capacitor). The higher the frequency the less time there is for charge to build up on the plates of the capacitor and oppose further charges from flowing in the circuit More charge is transferred in one second so the current is larger. Strathaven cademy Electricity and Electronics

7 Blocking DC (a) dc supply 2 V DC The lamp does not light. 2.5 V Lamp 1000 µf capacitor Current flows only while the capacitor charges. In this circuit, this takes a matter of milliseconds! This short burst of current is not sufficient to light the lamp. When the capacitor is charged, the current in the lamp is zero so it does not light 2 V C (b) ac supply (50 Hz) The lamp lights continuously. 2.5 V Lamp 1000 µf capacitor The alternating supply voltage pushes current one way then quickly reverses and pushes it the opposite way. Current flows on and off the plates of the capacitor continuously, causing an alternating current in the lamp which therefore lights. Learning point: capacitor blocks dc but can allow ac to flow in a circuit. Use of capacitor to block dc while passing ac Blocking capacitors are used to connect the different stages of amplification in a power amplifier. They are so called because they allow the ac (audio) signals to flow from one stage of amplification to the next while blocking the dc voltages which are present in the preceding stage. These dc voltages must not be amplified or they would ultimately be large enough to destroy the loudspeaker connected to the output stage. Technicians examining ac signals in an item of electronic equipment often find that the ac trace is thrown off the top of the CRO screen by the presence of a large dc voltage in the circuit. By pushing in the ac switch on the front of the CRO, a capacitor is placed in series with the input. This capacitor blocks the dc voltage leaving the ac signal displayed conveniently in the centre of the screen. Strathaven cademy Electricity and Electronics

8 pplications of Capacitors (for background interest) Blocking capacitor capacitor will stop the flow of a steady d.c. current. This is made use of in the a.c./d.c. switch in an oscilloscope. In the a.c. position a series capacitor is switched in allowing passage of a.c. components of the signal, but blocking any steady d.c. signals. Flashing indicators low value capacitor is charged through a resistor until it acquires sufficient voltage to fire a neon lamp. The neon lamp lights when the p.d. reaches 100 V. The capacitor is quickly discharged and the lamp goes out when the p.d. falls below 80V. 120 V 1-2 M Crossover networks in loudspeakers In a typical crossover network in low cost loudspeaker systems, the high frequencies are routed to LS-2 by the capacitor. L S 1 L S 2 Smoothing The capacitor in this simple rectifier circuit is storing charge during the half cycle that the diode conducts. This charge is given up during the half cycle that the diode does not conduct. This helps to smooth out the waveform. I C a p a c i t o r c h a r g e s C a p a c i t o r d i s c h a r g e s Capacitor as a transducer parallel plate capacitor can be used to convert mechanical movements or vibration of one of its plates into changes in voltage. This idea forms the basis of many measuring systems, e.g. by allowing a force to compress the plates we have a pressure transducer. t Strathaven cademy Electricity and Electronics

9 CTIVITY 13 Title: Current and frequency in a capacitive circuit im: To find how changing the frequency of the ac supply affects the current flowing in a circuit containing a capacitor. pparatus: Signal generator (Unilab ) Digital ammeter (200 m ac) nalogue voltmeter (10 V ac) Capacitor (100 microfarad; non-polar) Five connecting leads Circuit: Initial set up: V Connect the Lo output of the signal generator in series with the ammeter and capacitor using three of the connecting leads. Connect the voltmeter in parallel with the capacitor using the remaining two leads. Set the range switch on the signal generator to x 10 Hz. Set the frequency control to 11 to give a frequency of 110 Hz. Using the amplitude control, set a voltage across the capacitor that results in an ammeter reading close to, but not exceeding, 200 m. You must ensure, by adjustment if necessary, that this voltage remains the same for the rest of the experiment. Obtaining results: Note the setting of the frequency control. Note the size of the current flowing in the circuit. Continue by setting lower frequencies on the signal generator. Use an appropriate format to show the relationship between the current and the frequency in a circuit containing a capacitor. Strathaven cademy Electricity and Electronics

10 Capacitors in Circuits 15. The circuit below is used to investigate the charging of a capacitor. 12 V 10 kω 2000 µf (a) (b) (c) (d) What is the response of the ammeter when switch S is closed? How can you tell when the capacitor is fully charged? What would be a suitable range for the ammeter? If the 10 kω resistor is replaced by a larger resistor, what will be the effect on the maximum voltage across the capacitor? 16. In the circuit below the neon lamp flashes at regular intervals. The neon lamp requires a potential difference of 100 V across it before it will conduct and flash. It continues to glow until the potential difference across it drops to 80 V. While lit, its resistance is very small compared with R. R 120 V dc C (i) (ii) Explain why the neon bulb flashes. Suggest two methods of decreasing the flash rate. Strathaven cademy Electricity and Electronics

11 18. The circuit below is used to charge and discharge the capacitor V 1 2 V V R C (a) What position should the switch be set (i) to charge and (ii) to discharge the capacitor? (b) Draw graphs of V R against time for the capacitor charging and discharging, and of V C against time for the capacitor charging and discharging. (c) If the capacitor has capacitance of 4.0 µf and the resistor has resistance of 2.5 MΩ calculate: (i) the maximum charging current in the circuit above (ii) the maximum charge stored by the capacitor when fully charged in the above circuit MΩ 3 V 3 µf (a) (b) For the above circuit draw graphs of (i) V C against time during charging and (ii) V against time during charging. Calculate the final voltage across the capacitor and the final charged stored by it. 20. For each of the circuits below state what happens to the current flowing when the frequency is (i) increased and (ii) decreased. L o w v o l t a g e v a r i a b l e f r e q u e n c y s u p p l y C i r c u i t 1 C i r c u i t 2 Strathaven cademy Electricity and Electronics

12 21. In the circuit below the signal generator is set at 6.0 Vr.m.s., 1000 Hz. The lamp operates normally. Capacitors in Circuits S i g n a l g e n e r a t o r (a) (b) Explain why the lamp can operate normally when the plates of the capacitor are separated by an insulator. What happens to the brightness of the lamp when the frequency of the signal generator is increased. Why does this happen? 22. For each of the following circuits sketch a graph of current against frequency. S i g n a l g e n e r a t o r D i a g r a m D i a g r a m B 23. B S i g n a l g e n e r a t o r The supply frequency to the above circuit is increased from a very low frequency, while the supply voltage remains constant. What will happen to the brightness of lamp and B? Strathaven cademy Electricity and Electronics

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