Explain current, voltage and resistance conceptually, and compare energy transfer in series and parallel circuits

Learning goal: Explain conductors and insulators by how freely electrons move; define electric current as the rate of charge flow, with the ampere as one coulomb per second, and explain the convention that current is the flow of positive charge; explain potential difference (voltage) as the energy supplied per coulomb, with the volt as one joule per coulomb, and how a battery separates charge; explain how resistors oppose charge flow and transform electrical energy to other forms; reason about how current changes with voltage and resistance; and compare series and parallel circuits and where each is the better choice.

Charge, conductors and insulators. Every atom contains positive protons and negative electrons. In a conductor, such as any metal, some electrons are held so loosely by their nuclei that they move freely through the material, so charge can flow easily. In an insulator, such as plastic, rubber, glass or dry wood, electrons are held firmly by their atoms and cannot move through the material, so it does not carry current. The difference is a matter of how freely electrons move, not of whether the material contains electrons; both do. Earlier grades showed that a complete loop is needed for a circuit and that loops can be arranged in series or in parallel. This course explains what was observed with three ideas: current, voltage and resistance, treated conceptually; circuit calculations belong to a physics course.

Current. Electric current is the rate at which charge flows past a point in a circuit. Its unit is the ampere (A), and one ampere is one coulomb of charge per second (1 A = 1 C/s), the coulomb being the unit of charge. In a metal wire the moving charges are electrons, which are negative. By a convention that dates from before electrons were known, current is described as the flow of positive charge, so the conventional current arrows point from the positive terminal of a battery around the circuit to the negative terminal, while the electrons actually drift the opposite way. Both descriptions give the same results as long as one is used consistently. The electrons are already in the wire before the switch is closed; the power source does not supply them. It sets them moving all around the loop almost at once: the push spreads through the circuit at a large fraction of the speed of light, far too fast to notice in a classroom, which is why a bulb seems to light immediately even though individual electrons drift slowly.

Voltage. A battery contains a chemical reaction that separates charge, pushing electrons toward one terminal (negative) and leaving the other short of them (positive). Doing this is work, and it gives the electrons in the circuit electric potential energy. The potential difference or voltage across a source is the amount of energy supplied to each coulomb of charge: its unit is the volt (V), and one volt is one joule per coulomb (1 V = 1 J/C). A 9 V battery supplies 9 J of energy to every coulomb it pushes around the circuit. For an ideal source the voltage is a property of the source and does not depend on what is connected to it; a real battery comes close, but its voltage drops a little when it delivers a large current, and more as it runs down. A battery is made of cells joined together; a single cell gives a fixed potential difference set by its chemistry, and cells in series add their voltages, which is why a 9 V battery is a stack of cells. A source drives current because of the separation of charge it maintains; when the chemicals are used up, the separation stops and the battery is dead.

Resistance and the transfer of energy. A load is any component that takes energy from the circuit. A resistor is a load that opposes the rate of charge flow and turns the electrical energy into thermal energy (and, in a hot filament, light): a bulb filament, a heating element, a long thin wire. A motor is a load too, but most of the energy it takes becomes motion, not thermal energy. As charge passes through a resistor, the electrons transfer their electric potential energy to it, and the load transforms electrical energy into other forms: light and thermal energy in a bulb, thermal energy in a heater, motion and sound in a motor. The charge is not used up. The same current flows out of the resistor as into it; what the charge loses is energy, not quantity. A useful picture is a chain of buckets on a loop: the buckets go round and round, the pump at the source fills them, and each bucket empties at the device, but no bucket is ever destroyed. Confusing "the current is used up" with "the energy is transferred" is the most common error about circuits, and the bucket picture is the correction: the flow of electrons and the flow of energy are different things.

How current depends on voltage and resistance. With these three ideas the observations from earlier grades can be explained. Raising the potential difference pushes harder on the charges in the same circuit, so, with the resistance unchanged, charge flows at a greater rate: more coulombs pass each point every second, which is a larger current. Adding resistance opposes the flow more, so for the same source the current decreases. In words: current increases as potential difference increases and as resistance decreases. Two bulbs in series present more resistance than one, so the same battery drives a smaller current and both bulbs glow dimly. A thicker or shorter wire has less resistance than a thin or long one. Resistance matters in design: a circuit rated for a certain current can safely feed only so many lights; a short circuit, where insulation fails and current finds a path of very low resistance around the device, lets a very large current flow, which overheats wires and is why fuses and circuit breakers exist.

Series and parallel. In a series circuit there is one path: every component carries the same current, the source's voltage is shared among the components, and if any component fails by breaking the path (an open circuit) or is removed, the loop is broken and everything stops. In a parallel circuit the components are on separate branches: each branch receives the full voltage of the source, the current from the source splits among the branches and rejoins, and a break in one branch leaves the others working (a short circuit in one branch is different: it can blow the shared fuse and stop them all). A string of old-style holiday lights that all go out when one bulb fails is a series circuit; a house is wired in parallel so that switching off the kitchen light does not turn off the fridge, and each appliance gets the same voltage. A switch or fuse placed in series with the supply, before the circuit divides, controls or protects everything, even when the loads themselves are in parallel; parallel is the better choice for independent devices that each need the full voltage. Reading a circuit diagram, count the paths: one loop through every component is series; junctions where the path splits and rejoins are parallel.

A worked model: two bulbs, two ways. Suppose a battery, two identical bulbs, and connecting wire. Wired in series, the two bulbs form one loop; the battery's voltage is shared between them, the current through each is the same and smaller than with one bulb, so each glows dimly, and unscrewing either bulb darkens both. Wired in parallel, each bulb sits on its own branch across the battery, so each has the full battery voltage and glows as brightly as it would alone; the battery supplies the sum of the two branch currents, so it drains faster; and unscrewing one bulb leaves the other lit. A voltmeter across the battery reads nearly the same in both cases, because the source's voltage is a property of the source, not of the devices (a real cell's reading drops slightly when it supplies a large current); an ammeter in the main line reads more in the parallel case. This explains the classroom observation; no numbers beyond "more" and "less" are needed.

Investigation: find the faults and compare arrangements. Materials: two 1.5 V cells in a holder (a low-voltage source only), three identical bulbs in holders, connecting leads, a switch, a multimeter or separate ammeter and voltmeter, goggles. Steps: build one bulb in a loop with one cell and record the ammeter reading in the line and the voltmeter reading across the source, then power the same bulb from both cells in series and record both readings again, to see how the current changes as the potential difference increases; add a second bulb in series and record both readings and the brightness; rewire the two bulbs in parallel and record readings and brightness; unscrew one bulb in each arrangement and record what happens; finally, take three pre-built "faulty" circuit boards from the teacher (an open switch, a broken lead, a bulb in a holder with a loose contact) and, using the meter, locate and fix each fault. Record: a table of arrangement, current in the main line, voltage across the cells, brightness, and what happened when a bulb was removed; a note of each fault and how the meter revealed it. A result that supports the claims: with the same cells, the voltage across them stays about the same whichever bulbs are connected or how they are arranged, and it roughly doubles when the second cell is added in series; the main-line current is smaller with two bulbs in series than with one and larger with two in parallel; removing a series bulb darkens both while removing a parallel bulb leaves the other lit. Safety: goggles; low-voltage cells only, never a wall outlet; do not connect the cells to each other with a bare wire, which is a short circuit that heats the wire and drains the cells; disconnect when not measuring. What the model cannot show: the meters show current and voltage but not the electrons themselves, so the direction convention cannot be checked by eye; the arrangement compares "more" and "less", and calculating expected values is left for physics.

Worked example 1 — reading the units. A current of 2.0 A means 2.0 C of charge passes a point each second, so in 10 s a total of 2.0 × 10 = 20 C has passed. A 9 V battery gives 9 J to each coulomb, so those 20 C carried 9 × 20 = 180 J of energy from the battery to the circuit's resistors, where it was transformed into light and thermal energy. These are readings of the definitions of the ampere (C/s) and the volt (J/C), not circuit calculations; the charge was not used up, the energy was transferred.

Worked example 2 — conductor or insulator, and the fault. A student's circuit does not work. The leads are copper, a conductor, but one lead is clipped to the plastic coating instead of the bare metal end. Plastic is an insulator: its electrons are held firmly and cannot flow, so the loop is broken at that point and no current flows anywhere in it. Moving the clip to the bare copper completes the loop. A voltmeter across the cells would have shown the source was fine; an ammeter in the line would have read zero, which pointed to a break.

Worked example 3 — predict the change in current. A bulb is connected to one cell and glows dimly. Adding a second cell in series raises the potential difference, so each coulomb has more energy and the current rises; the bulb brightens. Adding a second identical bulb in series instead adds resistance, so with the same source the current falls and both bulbs are dimmer than the single bulb was. Adding the second bulb in parallel leaves each bulb with the full voltage and brightness, and the source supplies more total current.

Worked example 4 — which arrangement for the job? A designer needs an alarm that sounds when a window opens. In one design a thin wire runs across the window as part of a series circuit with the alarm's control; opening the window breaks the wire, current stops, and the control detects the drop and sounds a separately powered siren. In a second design the sensor closes a switch on a parallel branch when the window moves, adding a new path that raises the current from the source, which the control detects. Both use a change in current in the circuit; the series version signals with a fall to zero, the parallel version with a rise. A house's lighting, by contrast, must be parallel so each lamp has the full voltage and works independently.

Representation task: two labeled schematics. Draw a series circuit with a battery, a switch and two bulbs, and a parallel circuit with the same components on two branches. On each, draw conventional current arrows from the positive terminal, mark with a small "e" and an arrow the direction electrons actually move, label where energy is supplied to the charge and where it is transferred out, and write under each diagram what happens to the other bulb when one is removed and why.

Independent performance: diagnose, compare and explain. Using a low-voltage cell holder, bulbs, leads and meters, carry out the investigation and write a report. Success criteria: a table gives main-line current, source voltage and brightness for one bulb, two in series and two in parallel; the report states in words how current changed with added resistance and with an added cell, and explains each change using potential difference and resistance; the source voltage is shown to stay about the same when the bulbs are rearranged with the same cells, with the reason; at least two faults on pre-built boards are located with the meter readings that revealed them and the fix described; and a closing paragraph explains why charge is not used up in a bulb while electrical energy is transferred and transformed into light and thermal energy, using the words coulomb, joule, current and resistor correctly.