Simple Circuits: Study Guide (Physics 2 11.2)

What a circuit is

In Topic 11.1 you saw that charge moves when a source keeps a potential difference across a conductor. A circuit is the arrangement that lets this happen continuously. It is built from circuit elements joined by wires:

• batteries (sources of emf), which keep a potential difference,
• resistors and lightbulbs, where energy is transferred out of the circuit,
• capacitors, which store separated charge (Topic 10.6),
• switches, which open or close a path,
• ammeters, which measure current, and voltmeters, which measure potential difference,
• wires, which connect everything. In this course wires are ideal unless a question says otherwise: there is no change in potential along a wire.

A circuit is made of one or more electrical loops. A loop is a path that starts at a point, goes through elements and wires, and comes back to the same point.

Closed, open and short circuits

Charge can flow continuously only around a closed loop: a complete path with no gap. Three words describe what is possible.

• Closed circuit. There is a complete loop that includes the source, so charges would be able to flow. Any switches in that loop must be closed.
• Open circuit. There is a break somewhere in the loop, for example an open switch, a loose connection or a broken filament. Charges cannot flow around it. Every element in that loop then has zero current, wherever the break is. The current does not “reach the gap and stop”: with no complete loop, there is no flow anywhere in that loop.
• Short circuit. There is a path along which charges can flow with no change in potential, usually a plain wire connected across an element such as a bulb or resistor. The two ends of the shorted bulb or resistor are joined by an ideal wire, so they are at the same potential. With no potential difference across it, it carries no current. Charges take the wire path instead.

A wire connected straight across a battery is a dangerous short circuit. Almost nothing limits the current, so the battery and wire can become very hot. You will see why in Topic 11.3.

Loops that share elements

A single element can be part of more than one loop. This is what makes circuits with branches different from a single chain of elements.

The points where three or more wires meet are called junctions. At a junction, the current can split between paths or combine. (Topic 11.7 shows how the currents at a junction are related.) Every loop that passes through a branch includes the elements in that branch.

When you count loops, include loops that do not contain the battery. A loop made of two bulbs in neighbouring branches is a real loop, even though it has no source in it.

Schematic symbols

A schematic diagram is a simplified drawing of a circuit using standard symbols. It shows which elements are connected to which, and nothing else. Figure 1 shows the symbols used in this course.

Rules for reading and drawing schematics:

• Variable elements are shown by a diagonal arrow drawn through the normal symbol. A variable resistor is a resistor that can be adjusted, as in a dimmer switch.
• Conventional current is used unless a question says otherwise. It leaves the positive terminal (the long line), goes around the external circuit and returns to the negative terminal.
• Wires are ideal. A line on a schematic has the same potential all along it. Its length, shape and corners do not matter.
• Junctions are often marked with a dot where wires join. Two wires that cross without a dot are not connected.
• An ammeter measures the current through a point, so it is placed in the loop: you break the wire and connect the ammeter into the gap, so all the charge passing that point goes through it. An ideal ammeter does not change the current.
• A voltmeter measures the potential difference between two points, so it is connected across an element, from one end to the other, without breaking the loop. An ideal voltmeter draws no current.

Arrangement changes behaviour

The properties of a circuit depend on how its elements are arranged, not just on which elements it contains. Take one battery and two identical bulbs:

• Wired one after the other in a single loop, the bulbs share one path. Unscrew either bulb and the loop opens, so both go out.
• Wired in separate branches, each bulb is in its own loop with the battery. Unscrew one and the other stays lit, because its loop is still closed.

Same parts, different behaviour. That is why a schematic must show the connections exactly.

Worked example 1: loops and switches

Question. Figure 2 shows a battery, bulb A, and two branches between junctions J₁ and J₂. One branch contains bulb B. The other contains switch S and bulb C. (a) With S closed, list every closed loop and the elements in each. Which elements are in more than one loop? (b) S is now opened. Which bulbs carry current?

1. (a) Start at the battery and look for every way to return to the start.
   • Loop 1: battery → A → J₁ → B → J₂ → battery.
   • Loop 2: battery → A → J₁ → S → C → J₂ → battery.
   • Loop 3 (no battery): J₁ → B → J₂ → C → S → J₁.
2. Each element appears in exactly two loops. The battery and A are in loops 1 and 2. B is in loops 1 and 3. S and C are in loops 2 and 3.
3. (b) Opening S breaks loops 2 and 3. Only loop 1 is still closed. It contains the battery, so A and B carry current. C is in no closed loop, so it carries no current.

Answer. (a) Three loops, as listed. Every element is in two of them. (b) A and B carry current; C does not.

Check. Opening S did not turn off A, because A is also in loop 1. Only elements that are in no remaining closed loop with the battery lose their current.

Worked example 2: adding a short circuit

Question. In Figure 2, S is closed and all three bulbs are lit. A student then connects a plain wire directly from J₁ to J₂. Which bulbs now carry current? Explain.

1. The new wire joins J₁ and J₂. An ideal wire has no change in potential along it, so J₁ and J₂ are now at the same potential.
2. Bulb B is connected between J₁ and J₂, so the potential difference across B is zero. The same is true of the branch containing S and C.
3. With no potential difference across them, B and C carry no current: they are short-circuited. Charges flow from J₁ to J₂ through the new wire instead.
4. Bulb A is still in a closed loop with the battery: battery → A → J₁ → wire → J₂ → battery. So A still carries current.

Answer. Only A carries current. B and C go out.

Check. It is tempting to say “B and C now share the current with the wire”. They cannot: a bulb only carries current if there is a potential difference across it, and the wire has removed it. (In Topic 11.3 you will see that the current through A also increases, because the loop has less resistance.)

Worked example 3: from a description to a schematic

Question. A desk lamp has a battery, an on/off switch, a dimmer (variable resistor) and a bulb, all in one loop. A student wants to measure the current in the bulb and the potential difference across it. (a) Draw the schematic, including the meters. (b) With the switch closed, the ammeter reads 0.25 A. How much charge passes through the dimmer in 1.0 minute?

1. (a) One loop: draw a rectangle of wire and put the battery, switch, variable resistor and bulb on it, in any order. The order does not matter in a single loop.
2. The ammeter must carry the bulb’s current, so put it in the loop. In a single loop, any position works.
3. The voltmeter must measure the potential difference across the bulb, so connect it across the bulb, with one lead on each side.
4. (b) In a single loop there is only one path, so the same current passes through every element (charge is conserved, as in Topic 11.1). ΔQ = IΔt = (0.25 A)(60 s) = 15 C.

Answer. (a) Figure 3 (any order of elements in the loop is correct). (b) 15 C.

Check. A common error is to put the ammeter across the bulb, side by side with it. An ideal ammeter acts like a plain wire, so that would short-circuit the bulb. Another is to put the voltmeter in the loop. An ideal voltmeter lets no charge through, so that would make an open circuit.

Common misconceptions

• “Current gets as far as the gap in an open circuit and stops there.” With a break anywhere in a loop, there is no current anywhere in that loop.
• “A short circuit means a very short wire.” It means a path with no change in potential across the element it bypasses. The wire can be any length.
• “A shorted bulb still gets some of the current.” With zero potential difference across it, it carries none.
• “The bulb nearest the positive terminal lights first or gets the current first.” In a single loop, the current is the same everywhere and starts everywhere at almost the same time.
• “Loops must contain the battery.” A loop through two branches with no source is still a loop. It matters later for Kirchhoff’s loop rule (Topic 11.6).
• “The drawing shows where the parts are on the bench.” A schematic shows connections only. Long wires, bends and positions make no difference.
• “Ammeters and voltmeters are connected the same way.” Ammeter: in the loop, current through it. Voltmeter: across the element, potential difference between its ends.

Where this leads

Next, Topic 11.3 links the current in an element to the potential difference across it through resistance, so you can calculate the currents in the circuits you can now draw. Continue with Topic 11.3, Resistance, Resistivity and Ohm’s Law. First test yourself with the practice questions, then use the revision notes and the topic checklist to consolidate.