P6: Circuit Basics
Circuit symbols, current, potential difference, resistance, Ohm's law, I-V characteristics and conductors.
Circuit Symbols
You must be able to recognise and draw standard circuit symbols used in circuit diagrams. These symbols allow anyone to understand a circuit without ambiguity.
Essential Circuit Symbols
- Cell — long line is the positive terminal, short line is negative
- Battery — two or more cells connected in series
- Resistor — rectangular box; opposes the flow of current
- Variable resistor — resistor with an arrow through it
- Lamp — circle with a cross inside
- Fuse — circle with a line through it; melts if current is too high
- LED — triangle with a line and two arrows; emits light when forward biased
- Diode — triangle with a line; allows current in one direction only
- Thermistor — resistor in a circle with a diagonal line; resistance changes with temperature
- LDR — resistor in a circle with two arrows; resistance changes with light
- Ammeter — circle with an A; measures current in series
- Voltmeter — circle with a V; measures potential difference in parallel
- Switch — open or closed; controls whether current can flow
Current
Electric current is the rate of flow of charge. In a metal, current is the flow of electrons. Current is measured in amperes (A) using an ammeter placed in series.
Key Facts About Current
- Current is the rate of flow of charge carriers
- Conventional current flows from positive to negative
- Electron flow is from negative to positive
- Current is conserved at a junction (Kirchhoff's first law)
- In a single closed loop, current is the same at every point
Charge and Current
Q = It
Q = charge in coulombs (C)
I = current in amperes (A)
t = time in seconds (s)
Worked Example
A current of 2 A flows through a lamp for 30 seconds. Calculate the charge that flows.
Q = It = 2 × 30 = 60 C
Potential Difference
Potential difference (p.d.) is the energy transferred per unit charge between two points in a circuit. It is measured in volts (V) using a voltmeter placed in parallel across the component.
Key Facts About Potential Difference
- Potential difference is the work done per unit charge
- A p.d. of 1 V means 1 J of energy is transferred per coulomb of charge
- The p.d. across a cell is the energy it supplies to each coulomb of charge
- The p.d. across a component is the energy transferred by each coulomb passing through it
Potential Difference
V = W / Q
V = potential difference in volts (V)
W = energy transferred in joules (J)
Q = charge in coulombs (C)
Worked Example
A battery supplies 120 J of energy to 10 C of charge. Calculate the potential difference.
V = W / Q = 120 / 10 = 12 V
Resistance
Resistance is a measure of how much a component opposes the flow of current. It is measured in ohms (Ω). A higher resistance means less current for a given potential difference.
Key Facts About Resistance
- Resistance = potential difference / current
- Components with higher resistance reduce current more
- Resistance is caused by collisions between electrons and ions in the material
- Heating a metal increases its resistance because ions vibrate more
Ohm's Law (V = IR)
V = IR
V = potential difference in volts (V)
I = current in amperes (A)
R = resistance in ohms (Ω)
Worked Example
A 6 V battery is connected across a 200 Ω resistor. Calculate the current.
I = V / R = 6 / 200 = 0.03 A
Worked Example
A current of 0.5 A flows through a lamp when the p.d. is 12 V. Calculate the resistance.
R = V / I = 12 / 0.5 = 24 Ω
I-V Characteristics Practical
The I-V characteristics of a component show how the current through it varies with the potential difference across it. This is investigated using a standard test circuit.
Method for Investigating I-V Characteristics
- Set up a circuit with a variable power supply, the component being tested, an ammeter in series, and a voltmeter in parallel across the component
- Vary the potential difference using the variable supply
- Record the ammeter and voltmeter readings for a range of p.d. values
- Reverse the power supply connections and repeat for negative values
- Plot a graph of current (y-axis) against potential difference (x-axis)
Always include both positive and negative p.d. values when investigating I-V characteristics to see if the component behaves differently in reverse.
Ohmic Conductors
An ohmic conductor has a resistance that does not change with current. At constant temperature, the current through an ohmic conductor is directly proportional to the potential difference across it.
Ohmic Conductor I-V Graph
- The I-V graph is a straight line through the origin
- The gradient represents 1/R (the inverse of resistance)
- The resistance is constant at all values of current and p.d.
- A resistor at constant temperature is an ohmic conductor
Filament Lamp
A filament lamp is a non-ohmic conductor. Its resistance increases as the current increases because the filament heats up.
Filament Lamp I-V Graph
- The I-V graph is a curve that levels off at higher currents
- As current increases, the filament gets hotter and its resistance increases
- The graph is symmetrical — the lamp behaves the same in both directions
- Increasing resistance limits the current even though p.d. continues to rise
Diode
A diode only allows current to flow in one direction. It has a very high resistance in the reverse direction.
Diode I-V Graph
- Current is zero for negative p.d. values (reverse bias — very high resistance)
- Current is approximately zero for small positive p.d. values
- Current rises sharply once the threshold p.d. (about 0.7 V for a silicon diode) is reached
- A LED is a diode that emits light when current flows in the forward direction
Remember that a diode only conducts in the forward direction. In the reverse direction, resistance is extremely high and current is effectively zero.
Comparing I-V Characteristics
| Component | I-V Graph Shape | Resistance | Reason |
|---|---|---|---|
| Ohmic conductor (resistor) | Straight line through origin | Constant | Temperature stays constant |
| Filament lamp | Curve, levelling off | Increases with current | Filament heats up, ions vibrate more |
| Diode | Zero current in reverse, sharp rise in forward | Very high in reverse, low in forward above 0.7 V | Diode only conducts in one direction |
Practice Questions
1. A current of 3 A flows through a heater for 2 minutes. Calculate the charge that flows through the heater.
Q = It = 3 × 120 = 360 C
2. A 9 V battery transfers 45 J of energy. Calculate the charge that flows.
Q = W / V = 45 / 9 = 5 C
3. A resistor has a constant resistance of 50 Ω. When the p.d. across it is 10 V, calculate the current.
I = V / R = 10 / 50 = 0.2 A
4. Explain why the resistance of a filament lamp increases as the current through it increases.
As current increases, the filament gets hotter. The metal ions vibrate more vigorously, making it harder for electrons to pass through, so resistance increases.
5. Describe the I-V characteristic of a diode.
In the reverse direction, current is zero because resistance is very high. In the forward direction, current is approximately zero until the threshold voltage (about 0.7 V), then current rises sharply as resistance drops.
🔬 Required Practical
Required Practical: Investigating I-V Characteristics
Aim: To investigate how the current through a resistor, a filament lamp, and a diode varies with the potential difference across each component.
Method: Set up a circuit with a variable power supply, the component being tested, an ammeter in series, and a voltmeter in parallel across the component. Vary the potential difference using the variable supply and record the ammeter and voltmeter readings for a range of p.d. values. Reverse the power supply connections and repeat for negative p.d. values. Plot a graph of current (y-axis) against potential difference (x-axis) for each component. For the diode, use a protective resistor in series to prevent damage from excessive current.
Variables: Independent: potential difference across the component. Dependent: current through the component. Control: temperature of the component (allow to cool between readings), same component used throughout each test.
Analysis: For a resistor, the I-V graph should be a straight line through the origin, showing current is directly proportional to p.d. (ohmic conductor). For a filament lamp, the graph curves and levels off at higher currents, showing resistance increases as the filament heats up. For a diode, current is zero in the reverse direction and only flows above a threshold voltage (~0.7 V) in the forward direction. The gradient of the I-V graph represents 1/R for the linear region.
Common exam questions: "Why must you allow the resistor to cool between readings?" — To keep the temperature constant, because resistance changes with temperature for most conductors. "Why does the filament lamp graph curve?" — As current increases, the filament gets hotter, ions vibrate more, and resistance increases, so the current does not increase proportionally with p.d. "Why is a protective resistor needed for the diode?" — To limit the current and prevent the diode from being damaged by excessive current in the forward direction.
🔢 Maths Skills
Mathematical Skills for this Topic
Rearranging V = IR: To find current: I = V / R. To find resistance: R = V / I. These rearrangements are used constantly in circuit calculations. Always ensure units are consistent: V in volts, I in amperes, R in ohms. Convert mA to A by dividing by 1000, and kΩ to Ω by multiplying by 1000.
Plotting and interpreting I-V graphs: Current goes on the y-axis and potential difference on the x-axis. For an ohmic conductor, the gradient = 1/R (steeper gradient means lower resistance). For a non-ohmic conductor, the gradient changes along the curve — the resistance at any point is found by dividing the p.d. by the current at that point (R = V/I), NOT from the gradient of the tangent. Include both positive and negative values on the x-axis for I-V characteristic graphs.
Calculating charge from Q = It: Time must be in seconds. Convert minutes by multiplying by 60. For example, a current of 0.5 A for 3 minutes: Q = 0.5 × 180 = 90 C.
Calculating energy from V = W/Q: Rearranging gives W = VQ. This tells you the energy transferred when charge Q flows through a potential difference V. For example, 5 C of charge flows through a 12 V battery: W = 12 × 5 = 60 J.
⚠️ Common Misconceptions
Watch Out!
Students often think that current is "used up" as it flows through a circuit. Wrong: Current gets used up by components in a circuit, so there is less current after a resistor than before it. Correct: Current is the same at every point in a series circuit. Charge is conserved — the same amount of charge flows per second through every component. It is energy that is transferred (used), not current. A resistor transfers energy from each coulomb of charge, but the number of coulombs per second remains the same.
Students often think that higher resistance always means less current regardless of the voltage. Wrong: A higher resistance always means less current, no matter what the voltage is. Correct: Current depends on both resistance AND potential difference (I = V/R). A high resistance can still carry a large current if the voltage is high enough. For example, a 1000 Ω resistor with 1000 V across it carries 1 A, while a 10 Ω resistor with only 1 V across it carries just 0.1 A. You must consider both V and R together.
✍️ 6-Mark Question
Extended Answer Question
6 marks: Compare the I-V characteristics of an ohmic resistor, a filament lamp and a diode. Explain the differences.
An ohmic resistor (at constant temperature) has a straight-line I-V graph passing through the origin. The current is directly proportional to the potential difference, which means the resistance is constant. This is because the temperature of the resistor stays constant, so the arrangement of ions in the material does not change and electrons can flow through with the same ease at all currents.
A filament lamp has a curved I-V graph that levels off at higher currents. At low p.d., the graph is roughly linear, but as the p.d. and current increase, the curve bends over. This happens because the filament heats up as more current flows. The metal ions in the filament vibrate more vigorously at higher temperatures, making it harder for electrons to pass through. The resistance therefore increases with current, limiting further increases in current even as the p.d. continues to rise. The graph is symmetrical about the origin because the lamp behaves the same regardless of the direction of current.
A diode has a very different I-V characteristic. In the reverse direction (negative p.d.), the current is effectively zero because the diode has extremely high resistance. In the forward direction, the current is approximately zero until the threshold voltage (about 0.7 V for a silicon diode) is reached. Above this voltage, the current rises very sharply as the resistance drops dramatically. The diode only allows current to flow in one direction, making it useful for converting AC to DC.
Mark scheme: 2 marks for describing the ohmic resistor (straight line, constant resistance), 2 marks for describing the filament lamp (curve, increasing resistance with temperature), 2 marks for describing the diode (one direction only, threshold voltage)
📊 AO3: Analyse & Evaluate
Analysis and Evaluation
A student measured the current through an unknown component at different potential differences. The results are shown below:
| P.d. (V) | Current (mA) |
|---|---|
| -3.0 | 0 |
| -2.0 | 0 |
| -1.0 | 0 |
| 0.0 | 0 |
| 0.5 | 0 |
| 0.7 | 2 |
| 1.0 | 28 |
| 1.5 | 85 |
| 2.0 | 160 |
Identify the component and calculate its resistance at 1.5 V.
Answer: The component is a diode. The evidence is that no current flows in the reverse direction (negative p.d.), and current only begins to flow above approximately 0.7 V in the forward direction, then rises sharply. This matches the I-V characteristic of a silicon diode. Resistance at 1.5 V: R = V/I = 1.5 / 0.085 = 17.6 Ω (to 2 s.f. = 18 Ω). Note that the current must be converted from mA to A (85 mA = 0.085 A) before using Ohm's law.
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