0625 · 4.3Electric circuits

Circuit quantities and component symbols

0:00One failed bulb can switch off a whole string of decorations, while a broken bedroom lamp leaves the kitchen lights working. The difference is the arrangement of the circuit. Understanding that arrangement lets you predict current, potential difference and the behaviour of components. We will build that understanding by following charge around complete paths and tracking the energy it transfers. Current is the rate of flow of electric charge. Potential difference is the energy transferred per unit charge between two points.

0:27Resistance describes how difficult it is for current to flow through a component. A source supplies energy to the circuit, but components do not use up the charge passing through them. Electromotive force means the energy supplied by a source per unit charge. Despite its name, it is not a force, and it is measured in volts. We will use conventional current, flowing from the positive terminal through the external circuit towards the negative one.

0:52These ideas are enough to start interpreting circuit diagrams. A circuit diagram shows electrical connections rather than the physical positions of objects. Straight lines represent connecting wires, and standard symbols represent components. A filled dot identifies a junction where wires connect. Wires crossing without a junction dot should not be interpreted as connected. A cell is drawn as one long line beside a shorter one. The longer line represents its positive terminal, and several cells together form a battery.

1:22A power supply provides electrical energy from an external source. A generator converts mechanical energy into electrical energy, although its operating principle belongs in electromagnetic effects. A switch controls whether there is a complete conducting path. An open switch breaks the path, so no steady current flows around that loop. A closed switch completes it, allowing current to flow. Closing a switch does not create charge; it lets the free electrons already present in the circuit move.

1:49A fixed resistor provides resistance that is approximately constant under its intended operating conditions. Its symbol is a rectangle, while a variable resistor adds a diagonal arrow across that rectangle. Adjusting a variable resistor changes its resistance. With the supply voltage unchanged, increasing the circuit resistance reduces the current. A heater transfers electrical energy into thermal energy, while a lamp produces light and also transfers energy by heating. A motor transfers electrical energy into mechanical energy.

2:21A bell produces sound when operated electrically. Their different effects do not change the basic rule that each needs an appropriate supply and a complete circuit. A thermistor is a resistor whose resistance changes with temperature. Here we use only the negative temperature coefficient type, whose resistance decreases as it gets hotter. A light dependent resistor responds to illumination instead. Its resistance decreases as light intensity increases, making both components useful for sensing changing conditions.

Measuring instruments and special components

2:51An ammeter measures current and must be connected in series with the component being investigated. This makes the same current pass through both. Its resistance is very small, so it changes that current as little as possible. Connecting an ammeter directly across a supply can produce a dangerously large current. A voltmeter measures potential difference and connects in parallel across a component. Its two connections compare the energy per unit charge at the component’s ends.

3:17Its resistance is very large, so it draws very little current. A voltmeter placed in series would greatly reduce the circuit current and fail to measure the intended potential difference. A magnetising coil produces a magnetic field when current flows through it. A transformer has two coils and transfers energy between circuits using a changing magnetic field. It can increase or decrease an alternating voltage. Detailed explanations of coils and transformers belong in the video on electromagnetic effects.

3:46A fuse contains a conductor that melts when the current becomes excessive, breaking the circuit. A relay uses an electromagnet to operate switch contacts in another circuit. Current in its coil attracts a movable armature, changing the contact position. This allows one circuit to control another without directly connecting their conducting paths. Diodes and light emitting diodes are Supplement content for Extended students. A diode allows current in one direction and blocks it in the opposite direction under normal operating conditions.

4:15The bar in its symbol marks the cathode. Conventional current can pass through a forward biased diode from its anode towards its cathode. A light emitting diode emits light when it conducts in the forward direction. It is drawn as a diode symbol with arrows pointing outwards, representing emitted light. It normally needs a suitable series resistor to limit current. Compare these with the inward arrows on a light dependent resistor.

Series circuit rules and calculations

4:40In a series circuit, components are connected along one path without branching. Construct one by connecting the components end to end, then completing the loop through the source. The current at every point in a series circuit is the same. Every charge travelling around the loop must pass through each component. A resistor does not consume some current and leave less for the next one. If charge entered a component faster than it left, a growing amount would build up there.

5:05That does not happen in a steady circuit. Instead, components transfer energy from the charges while the rate of charge flow remains unchanged. Sources connected in series have a combined electromotive force determined by their orientations. When their polarities support the same current direction, add their electromotive forces. Three cells supplying one point five volts each therefore supply four point five volts together. If one identical cell is reversed, it opposes the other two, giving one point five volts overall.

5:35The combined resistance of resistors in series is the sum of their individual resistances. Charge encounters every resistor along the single route, so each adds to the overall opposition to current. For our three ohm and six ohm resistors, total resistance equals 3 + 6. That gives nine ohms. We can calculate the current using a nine volt supply and those two resistors. First, their combined resistance is nine ohms.

6:00Current equals potential difference divided by resistance, so nine volts divided by nine ohms gives one ampere. Because there is only one path, one ampere passes through each resistor. The rules about sharing potential difference are Supplement content for Extended students. Potential difference equals current multiplied by resistance, so the three ohm resistor has three volts across it. The six ohm resistor has six volts across it. Adding these potential differences gives nine volts, equal to the supply potential difference.

6:31This addition follows from energy conservation. Each unit of charge receives energy from the source, then gives it up while passing through the components. The total potential difference across the components in series equals the sum of their individual potential differences. We assume negligible resistance in the connecting wires and the source for these calculations.

Parallel circuit rules and calculations

6:51In a parallel circuit, components lie in separate branches connected between the same two junctions. Construct one by connecting one end of each branch to the same supply terminal. Connect their other ends to the other terminal. Charge now has more than one possible route through the circuit. For a parallel circuit, the current from the source is larger than the current in each conducting branch. At a junction, some charge takes one route while the rest follows another.

7:17After the branches rejoin, their currents combine. The source supplies all the branches, not just one of them. For Extended students, the precise rule is that the sum of currents entering a junction equals the sum leaving it. This follows from conservation of charge. Charge cannot disappear at the junction or build up there continuously in a steady circuit. If five amperes enters and two amperes takes one branch, three amperes must flow through the other.

7:42The potential difference across a set of parallel resistances is the same as across any one branch. Both ends of every branch connect to the same pair of junctions. Each branch therefore spans the same difference in energy per unit charge. Parallel branches share potential difference, but their currents need not be equal. Let us calculate the currents for the twelve volt parallel circuit shown. The six ohm branch has twelve volts across it, so its current is 12 ÷ 6, giving two amperes.

8:09The three ohm branch also has twelve volts, giving 12 ÷ 3, or four amperes. The source current is 2 + 4, giving six amperes. Adding a parallel branch gives charge another conducting route. For the same supply voltage, the source can therefore deliver more current. The combined resistance of two resistors in parallel is less than that of either resistor by itself. Even a branch with a relatively large resistance provides an additional route.

8:36Calculating that combined resistance is Supplement content. The reciprocal of the combined resistance equals the reciprocal of the first resistance plus the reciprocal of the second. This comes from adding the branch currents, each found by dividing their shared voltage by resistance. It expresses how the two conducting routes work together. For six ohms and three ohms, the reciprocal of combined resistance equals one sixth plus one third. Expressing both fractions in sixths gives one sixth plus two sixths, which equals one half.

9:06Taking the reciprocal gives a combined resistance of two ohms. This is smaller than either branch resistance, as expected. We can check that answer independently using the whole circuit. The source provides twelve volts and supplies six amperes. Combined resistance equals twelve volts divided by six amperes, giving two ohms again. Agreement between the two methods helps confirm that we have interpreted the connections correctly. Lighting circuits use parallel connections so that each lamp receives the full supply potential difference.

9:36Individual lamps can be switched independently using switches in their own branches. If one lamp fails and opens its branch, the others still have complete paths. In series, a broken lamp interrupts the only route.

Potential dividers and circuit recap

9:48Potential dividers use the way series components share the supply voltage. The Core starting point is that potential difference across a conductor increases as its resistance increases for a constant current. Potential difference equals current multiplied by resistance. Therefore, when two resistors carry the same current, the larger resistance has the greater potential difference. The potential divider equation is Supplement content for Extended students. The first resistance divided by the second resistance equals the first potential difference divided by the second potential difference.

10:21Both resistors carry the same current, so that common value cancels when we compare the voltages. The resistance ratio therefore determines the voltage ratio. The two potential differences must also add to the supply voltage. Combining those ideas gives a convenient calculation: voltage across the second resistor equals supply voltage multiplied by its resistance divided by total resistance. This is not a separate physical rule. It simply describes that resistor’s share of the series voltage.

10:50Consider a twelve volt supply across resistors of two thousand ohms and four thousand ohms. Their total resistance is six thousand ohms. The current is 12 ÷ 6000, giving zero point zero zero two amperes. That same current passes through both resistors because they are connected in series. The voltage across the four thousand ohm resistor equals 0.002 × 4000, giving eight volts. The other resistor therefore has 12 − 8, giving four volts.

11:18The resistances are in the ratio one to two, and the voltages have the same ratio. Greater resistance receives a greater share of the supply voltage. A variable potential divider has a movable contact along a resistive track connected across a supply. The contact divides the track into two resistances. Moving it changes their ratio and therefore alters the output voltage. When the output is taken between the contact and the lower end, sliding towards the upper end raises it.

11:46This differs from using a variable resistor simply to change the resistance of one current path. A potential divider selects a fraction of the supply voltage. An ideal unloaded divider can vary its output from zero up to the supply voltage. Our simple calculations assume the output does not draw significant current. An exam may replace one divider resistor with a thermistor or a light dependent resistor. Suppose the thermistor is the lower component and the output is measured across it.

12:14As temperature increases, its resistance decreases, so its share of the supply voltage decreases. Always identify which component the output spans before predicting the change. For an exam style question, describe the effect of heating that thermistor on the output potential difference. A clear answer gives each link separately. The thermistor’s resistance decreases as its temperature increases. Its resistance becomes a smaller fraction of the total, so the output potential difference across it decreases.

12:43Another question might ask you to explain why the total current entering a junction equals the total leaving it. State that electric charge is conserved. State that charge does not accumulate at the junction in a steady circuit. Therefore, charge flows out of the junction at the same total rate that it flows in. The most useful protection against mistakes is to trace connections rather than judge the appearance of a diagram.

13:06Series components have no branching between them, while parallel branches join the same two junctions. Do not add parallel resistances directly or assume their currents are equal. In divider questions, constant current is essential when comparing voltage directly with resistance. A circuit diagram is a map of paths for charge and transfers of energy. Series circuits have one current, added resistances and potential differences that add to the supply. Parallel circuits have a shared potential difference, branch currents that add and a reduced combined resistance.

13:38Potential dividers use resistance ratios to control how the supply voltage is shared.