16. Capacitors (2026) notes NJC

National Junior College Science Department | Physics 1 16. Capacitors (Extension to the topic of “Electric fields” and “Current and Circuits”) Content Page Learning Objectives ...................................................................................................................... 1 16.1 Capacitance .......................................................................................................................... 2 16.1.1 Charging and discharging a capacitor ............................................................................ 3 16.1.2 The meaning of capacitance .......................................................................................... 4 16.1.3 Energy stored in a capacitor .......................................................................................... 5 16.1.4 Capacitance of isolated bodies ...................................................................................... 7 16.2 RC circuits ............................................................................................................................ 8 16.2.1 Capacitors in series and in parallel ................................................................................ 8 16.2.2 Sharing charge and energy .......................................................................................... 11 16.2.3 RC circuits with constant e.m.f. source ........................................................................ 13 16.3 Some applications of capacitors ......................................................................................... 17 Exercise 1 ................................................................................................................................... 19 LEARNING OBJECTIVES Capacitance (a) Define capacitance as the ratio of the charge stored to the potential difference and use C= QV to solve problems. (b) Recall that the electric potential energy stored in a capacitor is given by the area under the graph of potential difference against charge stored, and use this and the equations U= 12 QV, U= 12Q2C, and U= 12 CV2 to solve problems. RC circuits (c) Solve problems using the formulae for the combined capacitance of two or more capacitors in series and in parallel. (d) Describe and represent the variation with time, of quantities like current, charge and potential difference, for a capacitor that is charging or discharging through a resistor, using equations of the form x=x0e!t! or x=x0#1−e!t!%, where 𝜏= RC is the time constant.

National Junior College Science Department | Physics 2 16.1 CAPACITANCE (a) Define capacitance as the ratio of the charge stored to the potential difference and use C= QV to solve problems. (b) recall that the electric potential energy stored in a capacitor is given by the area under the graph of potential difference against charge stored, and use this and the equations U= 12 QV, U= 12Q2C, and U= 12 CV2 to solve problems. Most electronic devices, such as radios, computers and MP3 players, make use of components called capacitors. Capacitors are used to store energy in electrical and electronic circuits and then they gradually release this energy if there is a power failure, so that the computer will operate long enough to save valuable data. Fig. 16.1a shows a variety of shapes and sizes of capacitors. (source: https://history.fnal.gov/historical/art_arch/captree.html) (a) (b) Fig. 16.1 Capacitors are usually quite small but Fig. 16.1b shows a giant capacitor, specially constructed to store electrical energy at the Fermilab particle accelerator in the United States. Every capacitor has two leads, each connected to a metal plate. To store energy, these two plates must be given equal and opposite electric charges. Between the plates is an insulating material called the dielectric (note: dielectric is not required for H2 Physics). Fig. 16.2 shows a simplified version of the construction of a capacitor and the spiral ‘Swiss-roll’ form of capacitor in practice. Fig. 16.2

National Junior College Science Department | Physics 3 16.1.1 Charging and discharging a capacitor Charging the capacitor Consider a pair of parallel plates separated by a vacuum gap and connected to a power supply. Connecting the capacitor to a supply pulls charge +Q from one plate and transfers it to the other, leaving behind charge –Q (In reality, electrons are moved onto one plate making it negatively charged while the other plate becomes positively charged). The supply does work in separating the charges. Fig. 16.3 shows the separation of charges and the flow of electrons round the circuit. • Current stops when the potential difference (p.d.) across the capacitor is equal to the e.m.f. of the supply. We then say that the capacitor is “fully charged”. • Since the two plates now store equal and opposite charges, the total charge on the capacitor is zero. When we talk about the “charge stored” by a capacitor, we refer to the magnitude of the charge Q stored on each plate. • To make the capacitor plates store more charge, we can use a supply of higher e.m.f. Discharging the capacitor If we connect the leads of the charged capacitor together, electrons flow back towards the positive plate around the circuit and the capacitor is discharged. We can also connect the charged capacitor to other electrical components, as shown in Fig. 16.4. When the switch closes, electrons will flow through the components and the capacitor discharges and its p.d. decreases. At any instant, VC=VR+VL Fig. 16.3 Fig. 16.4

National Junior College Science Department | Physics 4 16.1.2 The meaning of capacitance Fig. 16.5 shows a capacitor marked with the value 2200 𝜇F which is known as the capacitance. The capacitance of a capacitor is defined as Capacitance is the charge per unit potential difference across the plates where the charge refers to the charge on one plate. The mathematical relation, from the definition, is C=QV (eq. 16.1) where C is the capacitance of the capacitor, Q is the magnitude of the charge on each of the plate, V is the potential difference across the capacitor. The SI derived unit of capacitance is the farad (F). From eq. 16.1, 1 F = 1 C V−1 In practice, a farad is a large unit. Few capacitors have a capacitance of 1F. Capacitors usually have their values marked in picofarads (pF), nanofarads (nF) or microfarads (𝜇F). Besides the capacitance value, there are other markings on capacitors: • Highest safe working voltage. If you exceed this value (16 V for the capacitor in Fig. 16.5), charge may leak across between the plates and the dielectric will cease to be an insulator. • Polarity. Some capacitors must be connected correctly in a circuit. They have an indication to show which end must be connected to the positive or negative end of the supply (see the blank band with a negative sign in Fig. 16.5). Failure to connect correctly will damage the capacitor, and can be extremely dangerous. MUST MEMORISE! Fig. 16.5

National Junior College Science Department | Physics 5 16.1.3 Energy stored in a capacitor When you charge a capacitor, you use a power supply to push electrons onto one plate and off the other. The power supply does work on the electrons, so their potential energy increases. You recover this energy when you discharge the capacitor. In order to charge a capacitor, work must be done to push electrons onto one plate and off the other (Fig. 16.6a). At first, there is only a small amount of negative charge on the left-hand plate. Adding more electrons is relatively easy, because there is not much repulsion. As the charge on the plate increases, the repulsion between the electrons on the plate and the new electrons increases, and a greater amount of work must be done to increase the charge on the plate. Fig. 16.6b shows how the p.d. V increases as the amount of charge Q increases. It is a straight line b