0625 · 4.2Electrical quantities

Charge, electrostatics and conductors

0:00A rubbed balloon can attract small pieces of paper, while a battery can make a lamp shine. Both effects involve electric charge, but charge and energy are different things. In this video, we will connect charge, current, voltage, resistance and power. You will understand what each quantity measures, how we measure it, and why the equations work. We need only a small amount of atomic knowledge. Atoms contain positively charged protons and negatively charged electrons.

0:26An atom is neutral when these charges balance. In the solid materials we discuss, electrons can transfer between objects, but protons remain within their atoms. This distinction explains both charging by friction and electrical conduction in metals. There are two types of electric charge, positive and negative. Positive charges repel other positive charges, and negative charges repel other negative charges. Positive charges attract negative charges. Repulsion means a force pushes objects apart, while attraction means a force pulls them together.

0:57These forces can act without the charged objects touching. An object becomes negatively charged when it gains electrons, because it now has excess negative charge. An object becomes positively charged when it loses electrons, leaving excess positive charge. Becoming positive does not mean gaining protons. Charging solids by friction involves only a transfer of negative charge, carried by electrons. Rub a suitable plastic rod with a dry cloth, then bring the rod near tiny pieces of paper.

1:23The paper moves towards the rod, showing an electrostatic effect. For a plastic and cloth combination that transfers electrons to the rod, the rod becomes negative. The cloth loses those electrons and becomes positive; friction does not create charge. To show repulsion, suspend a charged plastic rod from an insulating thread so that it can turn freely. Charge a second identical rod using the same method, then bring it close.

1:47The rods repel because they have the same type of charge. Using rods with opposite charges demonstrates attraction instead, provided their charge signs are known. An electroscope detects electric charge. It has a conducting cap connected to a metal stem and a thin conducting leaf. Touch the cap with a charged rod so that charge transfers to the electroscope. The stem and leaf acquire the same type of charge, so they repel and the leaf rises.

2:11Attraction alone does not prove that both objects have opposite charges. A charged rod can attract neutral paper because the charges within the paper shift slightly. The nearer side then experiences a stronger attraction than the repulsion on the farther side. Repulsion is therefore the clearer test that an object is charged. A conductor allows electric charge to move through it easily. Metals such as copper and aluminium contain free electrons that can move throughout the material.

2:35Insulators, such as plastic, glass and rubber, do not have electrons free to move throughout them. Their electrons remain bound, so charge cannot flow through them easily. To distinguish conductors from insulators, make a low-voltage circuit containing a cell, a lamp and a gap between two clips. First connect the clips directly to check that the lamp works. Then place a sample between them, ensuring good contact. A conductor completes the conducting path and lights the lamp; an insulator leaves it unlit.

3:02For this experiment, compare dry samples of copper, aluminium, plastic and rubber. Keep the cell, lamp and connections unchanged, so the material is the main difference. Use a low-voltage supply, never the mains. The electron model explains the results: metal samples provide mobile charge carriers, whereas the insulating samples do not.

Electric fields and field patterns

3:22The next ideas are Supplement content for Extended students. Electric charge is measured in coulombs. An electric field is a region in which an electric charge experiences a force. This lets us describe how a charged object affects the space around it, rather than imagining that contact is needed. The direction of an electric field at a point is the direction of the force on a positive charge at that point.

3:42A negative charge experiences a force in the opposite direction. Field lines are a drawing convention for representing this pattern. Their arrows show the field direction, not necessarily the movement of every charged particle. Around a positive point charge, the field points radially outwards. A small positive charge placed anywhere nearby would be pushed directly away from it. Around a negative point charge, the field points radially inwards, because a positive charge would be attracted.

4:08The pattern is symmetrical because no direction around an isolated point charge is preferred. Outside an isolated charged conducting sphere, the field also has a radial pattern. The lines meet the surface at right angles. For a positive sphere, arrows point away from its surface; for a negative sphere, arrows point towards it. Draw the field outside the sphere, with the arrow direction determined by a positive test charge. Between oppositely charged parallel conducting plates, draw straight, parallel, equally spaced field lines.

4:38The arrows point from the positive plate towards the negative plate. This represents a uniform field, meaning the field has the same strength and direction throughout the region shown. For this syllabus, you do not need to draw effects near the plate edges.

Current and charge flow

4:50Current connects charge to motion, and this basic idea belongs to Core content. Electric current is related to the flow of charge. In a metal, electrical conduction happens through the movement of free electrons. With a source connected across a complete conducting path, these electrons have an overall movement around the circuit. A direct current flows in one direction. An alternating current repeatedly changes direction. A cell provides direct current, while the mains supply provides alternating current.

5:17With alternating current, electrons do not travel all the way around the circuit. Instead, they move backwards and forwards each time the supply reverses. An ammeter measures current and must be connected in series with the component being investigated. This places it in the same path, so the component’s current passes through the meter. An analogue ammeter uses a pointer and scale, while a digital ammeter displays a number. For direct current, connect the meter terminals with the correct polarity.

5:44Begin with the highest suitable current range when the expected value is unknown. Then select a lower range, if appropriate, for a more precise reading without exceeding its limit. On an analogue meter, use the scale matching that range and view the pointer straight on. On a digital meter, check whether the display indicates amperes or milliamperes. The precise current definition is Supplement content. Electric current is the charge passing a point per unit time.

6:09Current equals charge divided by time. Charge is measured in coulombs, time in seconds and current in amperes. One ampere means one coulomb of charge passes the chosen point each second. Suppose twenty-four coulombs pass a point in eight seconds, and we need to calculate the current. We divide the total charge by the time because current measures the amount passing each second. 24 ÷ 8 gives three amperes. This means three coulombs pass that point every second on average.

6:36Another Supplement distinction concerns direction. Conventional current flows from positive to negative through the external circuit. Free electrons in metal flow from negative to positive, in the opposite direction. Conventional current was defined using positive charge, so its direction does not match electron movement. Use conventional current when adding arrows to circuit diagrams.

EMF, potential difference and voltmeters

6:57Electromotive force and potential difference describe energy transfer, rather than the amount of charge flowing. These definitions are Core content. Electromotive force is the electrical work done by a source in moving a unit charge around a complete circuit. Despite its name, electromotive force is not a force in newtons; it is measured in volts. Potential difference is the work done by a unit charge passing through a component. In other words, it tells us how much energy is transferred per coulomb passing through that component.

7:25Potential difference between two points is measured in volts. One volt means one joule of energy transferred per coulomb of charge. Think of charge as carrying an energy allowance supplied by the source. Electromotive force describes the energy supplied per coulomb, while potential difference across a component describes energy transferred there per coulomb. The component does not use up the charge. Instead, energy is transferred to the surroundings by light or heating, while charge continues through the circuit.

7:52The equations expressing these definitions are Supplement content. Electromotive force equals work done divided by charge. Potential difference also equals work done divided by charge. In both equations, work done is measured in joules and charge in coulombs. The equations look alike because both quantities measure energy transferred per unit charge. Suppose a source does sixty joules of electrical work while moving ten coulombs around a complete circuit. To calculate its electromotive force, divide the work done by the charge.

8:2060 ÷ 10 gives six volts. Each coulomb receives six joules from the source, which gives the numerical answer its physical meaning. Suppose those ten coulombs transfer forty joules while passing through one component. To find its potential difference, divide forty joules by ten coulombs. The answer is four volts, meaning four joules are transferred per coulomb in that component. The remaining energy is transferred elsewhere in the complete circuit, rather than disappearing.

8:46A voltmeter measures potential difference and is connected in parallel across the component. Its two connections allow it to compare the two ends. Analogue voltmeters use a pointer and scale, while digital voltmeters display the reading numerically. Choose a suitable range, beginning high if uncertain, and use the correct terminal polarity for direct voltage.

Resistance and current–voltage graphs

9:05Resistance tells us how much potential difference is needed to produce a particular current. The Core equation is resistance equals potential difference divided by current. Potential difference is measured in volts, current in amperes and resistance in ohms. A larger resistance means a smaller current for the same potential difference. To determine resistance experimentally, connect an ammeter in series with the test component and a voltmeter across it. Switch on the low-voltage supply and record both readings.

9:34Divide the measured potential difference by the measured current. Repeat at other suitable supply settings, keeping the component’s temperature as steady as possible when investigating constant resistance. For example, the voltmeter reads six volts and the ammeter reads zero point three amperes. We use the potential difference across the component, not a reading across some other part of the circuit. 6 ÷ 0.3 gives twenty ohms. This component therefore needs twenty volts per ampere at that operating condition.

10:00For metallic wires, greater length means greater resistance, while greater cross-sectional area means lower resistance. A longer wire gives moving electrons more metal to pass through. A thicker wire provides more space for charge to flow. Comparisons must use the same material and temperature, because those factors also affect resistance. The proportional relationships are Supplement content. Resistance is directly proportional to length and inversely proportional to cross-sectional area. Suppose a wire initially has a resistance of six ohms.

10:31Doubling its length gives twelve ohms, and then tripling its cross-sectional area reduces that to four ohms, with material and temperature unchanged. Current–voltage graphs are also Supplement content. Put current on the vertical axis and potential difference on the horizontal axis. A resistor of constant resistance has a straight line through the origin. Doubling the potential difference doubles the current, so their ratio remains constant; a steeper line means a lower resistance on these axes.

10:58For a filament lamp, the graph curves and becomes less steep as the magnitude of the potential difference increases. A greater current heats the filament, and its resistance increases. Electrons encounter greater opposition in the hotter metal, so current increases less rapidly. Reversing the potential difference gives the corresponding curve in the negative region. A diode conducts in one direction only in the simple model used here. Its current is negligible in the reverse direction, because its resistance there is very high.

11:25In the forward direction, current remains small initially, then rises sharply once the potential difference is sufficient. This happens because its resistance becomes low once forward conduction begins. Do not draw a diode graph as a straight line through the origin; its current and voltage are not directly proportional.

Electrical power, energy and recap

11:43Electrical energy and power return us to Core content. Circuits transfer energy from a source, such as a cell or mains supply, to components and then into the surroundings. Power is the rate of energy transfer. A lamp with greater electrical power transfers more energy each second, though not necessarily all of it as visible light. Power equals current multiplied by potential difference. Current tells us how many coulombs pass each second, while potential difference tells us how many joules are transferred per coulomb.

12:10Multiplying these quantities gives joules transferred each second. That is power, measured in watts, with one watt equal to one joule per second. Suppose a lamp takes zero point five amperes at twelve volts. Multiply zero point five by twelve to calculate its electrical power. The answer is six watts, meaning six joules are transferred every second. This is a rate of transfer, not the total energy used during an entire period.

12:35Energy equals current multiplied by potential difference multiplied by time, when current and potential difference remain constant. If the lamp operates for three minutes, first convert the time to one hundred and eighty seconds. Multiply six watts by one hundred and eighty seconds to calculate the energy. The answer is one thousand and eighty joules. Electricity bills commonly measure energy in kilowatt-hours rather than joules. One kilowatt-hour is the energy transferred by an appliance operating at one kilowatt for one hour.

13:04It is an energy unit, not a power unit. Since one kilowatt is one thousand watts, one kilowatt-hour equals three million six hundred thousand joules. Suppose a two-kilowatt heater operates for three hours, and electricity costs thirty pence per kilowatt-hour. Multiply two kilowatts by three hours to calculate six kilowatt-hours of energy. Then multiply six by thirty pence to obtain one hundred and eighty pence. The cost is one pound eighty, excluding any fixed charges.

13:31An exam may ask you to explain a filament lamp’s curved current–voltage graph rather than merely identify it. A precise answer links the changing temperature to resistance. Increasing current raises the filament’s temperature. Its resistance increases as it becomes hotter. The current therefore increases less rapidly as potential difference increases, making the graph less steep. Several mistakes come from treating all electrical quantities as interchangeable. Current measures charge flow per second, whereas voltage measures energy transferred per coulomb.

14:01An ammeter belongs in series, while a voltmeter belongs in parallel. Electrons are not used up by a lamp, and a kilowatt-hour measures energy rather than power. The complete picture begins with charge, which can attract or repel and can move through conductors. Current measures its rate of flow, while electromotive force and potential difference describe energy transfer per unit charge. Resistance connects potential difference to current. Power measures energy transferred each second, and multiplying by time gives the total transferred.