P5: Circuit Basics
Standard circuit symbols, current, voltage and resistance โ Ohm's Law and I-V characteristics.
P5 Circuit Basics
๐ Key Definitions
Electric current: The rate of flow of charge. Measured in amperes (A) using an ammeter connected in series. Current is the same in all parts of a series circuit.
Potential difference (voltage): The energy transferred per unit charge passing between two points. Measured in volts (V) using a voltmeter connected in parallel across the component.
Resistance: The opposition to the flow of current. Measured in ohms (ฮฉ). Higher resistance means less current for a given voltage.
๐ Standard Circuit Symbols
| Component | Symbol Description | Key Detail |
|---|---|---|
| Cell | Long line (+) and short thick line (-) | Provides energy to the circuit |
| Battery | Two or more cells joined together | Long line = positive terminal |
| Switch (open) | Gap in the circuit line | Circuit is incomplete โ no current |
| Switch (closed) | Line completes the circuit | Circuit is complete โ current flows |
| Lamp | Circle with a cross inside | Converts electrical energy to light |
| Resistor | Rectangle | Opposes current flow at constant rate |
| Variable resistor | Rectangle with diagonal arrow | Resistance can be changed |
| Ammeter | Circle with 'A' inside | Connected in series, measures current |
| Voltmeter | Circle with 'V' inside | Connected in parallel, measures voltage |
| Diode | Triangle pointing to a line | Current flows in one direction only |
| LED | Triangle with arrows (light) | Diode that emits light when forward biased |
| Fuse | Rectangle with line through it | Melts if current is too high, breaks circuit |
| Thermistor | Rectangle with 't' or diagonal line | Resistance decreases as temperature increases |
| LDR | Circle with arrows, rectangle inside | Resistance decreases as light intensity increases |
๐ Ohm's Law
Ohm's Law: The current through a resistor at constant temperature is directly proportional to the potential difference across it. This means V = I x R.
V = I x R
Where:
- V = potential difference, in volts (V)
- I = current, in amperes (A)
- R = resistance, in ohms (ฮฉ)
R = V / I
I = V / R
๐ I-V Characteristics
Required practical: Investigate the I-V characteristics of a resistor, a filament lamp and a diode to see how current varies with potential difference.
| Component | I-V Graph Shape | Explanation |
|---|---|---|
| Resistor (at constant temperature) | Straight line through origin | Current is directly proportional to voltage (Ohmic conductor). Resistance is constant. |
| Filament lamp | Curve that flattens at higher voltages | As current increases, the filament heats up, resistance increases, so current increases less quickly. Not an Ohmic conductor. |
| Diode | Current only in forward direction; zero in reverse | Diode only conducts when forward biased (positive to the anode). Very high resistance in reverse direction. |
Method for I-V Characteristics Practical
- Set up a circuit with a variable resistor (or variable power supply), ammeter in series, and voltmeter in parallel across the component.
- Vary the potential difference across the component from 0 V upwards in small steps.
- Record the current at each voltage.
- Repeat for negative voltages (reverse the power supply connections).
- Plot a graph of current (y-axis) against voltage (x-axis).
๐ก๏ธ Thermistors and LDRs
| Component | Condition | Resistance | Current |
|---|---|---|---|
| Thermistor | Temperature increases | Resistance decreases | Current increases |
| Temperature decreases | Resistance increases | Current decreases | |
| LDR | Light intensity increases | Resistance decreases | Current increases |
| Light intensity decreases | Resistance increases | Current decreases |
Applications: Thermistors are used in temperature sensors (e.g. thermostats, car engine temperature sensors). LDRs are used in light sensors (e.g. automatic street lights, burglar alarms, camera light meters).
๐ Worked Examples
Worked Example 1 โ Using Ohm's Law to find Voltage
Question: A resistor has a resistance of 10 ฮฉ and a current of 3 A flows through it. Calculate the potential difference across the resistor.
Solution:
V = I x R = 3 x 10 = 30 V
Worked Example 2 โ Using Ohm's Law to find Resistance
Question: A lamp has a potential difference of 12 V across it and a current of 0.5 A flows through it. Calculate the resistance of the lamp.
Solution:
R = V / I = 12 / 0.5 = 24 ฮฉ
Worked Example 3 โ Using Ohm's Law to find Current
Question: A 220 ฮฉ resistor is connected to a 6 V battery. Calculate the current flowing through it.
Solution:
I = V / R = 6 / 220 = 0.027 A = 27 mA
Worked Example 4 โ Thermistor Calculation
Question: A thermistor has a resistance of 5000 ฮฉ at 20 ยฐC. When heated to 80 ยฐC its resistance drops to 200 ฮฉ. It is connected to a 9 V battery. Calculate the current at each temperature.
Solution:
At 20 ยฐC: I = V / R = 9 / 5000 = 0.0018 A = 1.8 mA
At 80 ยฐC: I = V / R = 9 / 200 = 0.045 A = 45 mA
As temperature increases, resistance decreases and current increases.
Worked Example 5 โ LDR in a Circuit
Question: An LDR is connected in series with a 6 V battery and a lamp. In bright light the LDR has resistance 200 ฮฉ and the lamp has resistance 100 ฮฉ. In darkness the LDR resistance rises to 10 000 ฮฉ. Calculate the total current in each condition.
Solution:
Bright light: Total R = 200 + 100 = 300 ฮฉ. I = 6 / 300 = 0.02 A = 20 mA (lamp is on).
Darkness: Total R = 10 000 + 100 = 10 100 ฮฉ. I = 6 / 10 100 = 0.000594 A = 0.59 mA (lamp is very dim/off).
Worked Example 6 โ Explaining I-V Characteristics
Question: Explain why the I-V graph for a filament lamp is curved, not a straight line.
Solution: As the current through the filament lamp increases, the filament gets hotter. The increased vibration of the metal ions in the filament makes it harder for electrons to pass through, so resistance increases. This means that as voltage increases, the current does not increase proportionally โ the graph curves and flattens. The filament lamp is not an Ohmic conductor because its resistance changes with temperature.
โ Practice Questions
Q1: Foundation Name the component that measures current and state how it is connected in a circuit.
Q2: Foundation A resistor has 8 V across it and a current of 2 A flows through it. Calculate its resistance.
Q3: Foundation Describe the difference between the I-V graph of a resistor and a filament lamp.
Q4: Higher A thermistor is connected to a 5 V supply. At 25 ยฐC its resistance is 1000 ฮฉ. At 100 ยฐC its resistance is 100 ฮฉ. Calculate the current at each temperature and explain the difference.
Q5: Higher Explain why a diode only allows current to flow in one direction. How would this appear on an I-V graph?
Q6: Higher A student investigates the I-V characteristics of a resistor. They vary the voltage and measure the current. State one safety precaution and one way to improve accuracy.
โ Answers
- An ammeter measures current. It is connected in series with the component โ the current flows through it.
- R = V / I = 8 / 2 = 4 ฮฉ.
- A resistor (at constant temperature) gives a straight line through the origin โ current is directly proportional to voltage (Ohmic). A filament lamp gives a curved graph that flattens at higher voltages โ as current increases, the filament heats up and resistance increases, so current increases more slowly (non-Ohmic).
- At 25 ยฐC: I = 5 / 1000 = 0.005 A = 5 mA. At 100 ยฐC: I = 5 / 100 = 0.05 A = 50 mA. The current is much higher at 100 ยฐC because the thermistor's resistance decreases as temperature increases (more charge carriers are released), allowing more current to flow.
- A diode has very low resistance in the forward direction (allows current through) but very high resistance in the reverse direction (blocks current). On the I-V graph: there is current in the forward direction (positive voltage), rising steeply once the threshold voltage is exceeded. In the reverse direction (negative voltage), the current is essentially zero.
- Safety precaution: do not exceed the maximum voltage rating of the resistor to avoid overheating/burning out. Improving accuracy: take multiple readings and calculate a mean, or use smaller voltage increments to get more data points for a smoother graph.
๐ฏ Exam Tips
- Remember: ammeter in series, voltmeter in parallel โ this comes up frequently.
- When drawing circuit symbols, make sure you know the difference between a cell (one pair of lines) and a battery (multiple cells).
- Ohm's Law only applies to Ohmic conductors at constant temperature โ filament lamps and diodes do not obey Ohm's Law.
- For thermistor questions: hot = low resistance = high current. Cold = high resistance = low current.
- For LDR questions: bright light = low resistance = high current. Dark = high resistance = low current.
- When explaining a filament lamp graph, always mention increasing resistance due to increasing temperature.
- Current is the same in all parts of a series circuit โ this is a key rule for P6.
๐ฌ 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, ammeter in series with the component, and voltmeter in parallel across the component. Vary the p.d. from 0 V in small steps (e.g. 0.5 V intervals) and record the current at each voltage. Reverse the power supply connections to obtain negative voltage readings. Repeat for each component. Plot I-V graphs for each component.
Variables: IV: Potential difference across the component, DV: Current through the component, Control: Temperature of the component (allow to cool between readings), same circuit setup
๐ข Maths Skills
Mathematical Skills
You must be able to rearrange V = IR to find any unknown quantity. Remember: V = I ร R, I = V รท R, R = V รท I. Always check units โ current in amps, voltage in volts, resistance in ohms. Convert mA to A by dividing by 1000.
Maths Example
A component has a resistance of 470 ฮฉ and a current of 52 mA flows through it. Calculate the voltage.
I = 52 mA = 0.052 A
V = I ร R = 0.052 ร 470 = 24.44 V โ 24 V
โ ๏ธ Common Misconceptions
Watch Out!
1. Wrong: Current is "used up" as it goes around a circuit Correct: Current is the same everywhere in a series circuit โ energy is transferred, not charge
2. Wrong: Voltage flows through a circuit Correct: Current flows; voltage (potential difference) is measured across a component โ it is the energy per unit charge
3. Wrong: Resistance is "bad" and wastes energy Correct: Resistance is a property that opposes current; it is essential โ without resistance, current would be dangerously high
4. Wrong: Higher resistance means less energy is transferred Correct: Higher resistance means less current flows for a given voltage; the energy transferred per unit charge (V) is set by the supply
โ๏ธ 6-Mark Question
Extended Answer
6 marks: Compare the I-V characteristics of a resistor, a filament lamp and a diode. Include descriptions of the graph shapes and explanations for each.
A resistor at constant temperature is an Ohmic conductor. Its I-V graph is a straight line through the origin, meaning current is directly proportional to voltage. The resistance remains constant. A filament lamp is a non-Ohmic conductor. Its I-V graph is a curve that flattens at higher voltages. As current increases, the filament heats up, the metal ions vibrate more, and resistance increases, so current increases less quickly. A diode only allows current to flow in the forward direction (forward bias). On the I-V graph, current is zero in reverse bias and rises steeply once the threshold voltage (~0.6 V) is exceeded in forward bias. The diode has very high resistance in reverse and very low resistance in forward bias above the threshold.
Mark scheme: 1 mark โ resistor straight line / Ohmic, 1 mark โ resistance constant, 1 mark โ lamp curves / non-Ohmic, 1 mark โ resistance increases with temperature, 1 mark โ diode conducts in one direction only, 1 mark โ reference to threshold voltage or very high reverse resistance
๐ AO3: Analyse & Evaluate
Analysis and Evaluation
A student investigates the I-V characteristics of a component and records the following data:
| Voltage (V) | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|---|
| Current (A) | 0 | 0.10 | 0.18 | 0.24 | 0.28 | 0.30 | 0.31 |
(a) Plot a sketch of the I-V graph and state whether the component is Ohmic or non-Ohmic. Justify your answer.
(b) Calculate the resistance of the component at 1 V and at 6 V. Explain why the resistance changes.
(c) The student did not allow the component to cool between readings. Explain how this affects the validity of the results and suggest an improvement.
Answers: (a) The graph curves and flattens โ the component is non-Ohmic because current is not proportional to voltage. (b) At 1 V: R = 1/0.10 = 10 ฮฉ. At 6 V: R = 6/0.31 = 19.4 ฮฉ. Resistance increases because the component heats up (it is a filament lamp). (c) Not allowing cooling means temperature is an uncontrolled variable, reducing validity. Improvement: switch off the supply between readings and allow the component to return to room temperature, or use smaller voltage increments to minimise heating.
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