E2: Ohm's Law & Resistor Networks
Ohm's law, series and parallel resistor combinations, potential dividers
Ohm's Law & Resistor Networks
Ohm's law, series and parallel resistor combinations, potential dividers
Key Fact: In series, total resistance R_total = R1 + R2 + R3; the same current flows through each resistor.
Key Fact: In parallel, 1/R_total = 1/R1 + 1/R2 + 1/R3; the same voltage is across each resistor.
Key Fact: For two resistors in parallel: R_total = (R1 × R2)/(R1 + R2).
Key Fact: A potential divider uses two series resistors to produce a fraction of the supply voltage: V_out = V_in × R2/(R1 + R2).
Key Fact: In series circuits, voltage splits proportionally to resistance: the larger resistor gets the larger voltage share.
Key Fact: In parallel circuits, each branch carries current inversely proportional to its resistance.
Key Fact: Ohm's Law can be applied to each individual resistor in a network to find voltage or current.
Key Fact: Variable resistors (potentiometers) can be used in potential dividers to produce adjustable output voltage.
Key Fact: The total power dissipated in a network equals the sum of power in individual resistors.
Key Fact: Series circuits act as voltage dividers; parallel circuits act as current dividers.
Key Fact: When combining series and parallel sections, simplify the parallel parts first, then add series resistances.
Key Fact: A load across the output of a potential divider reduces the output voltage due to loading effects.
📋 Key Vocabulary and Concepts
For Ohm's Law & Resistor Networks, you must know:
- Series circuit: A circuit where components are connected end to end, carrying the same current.
- Parallel circuit: A circuit where components are connected across the same two points, sharing the same voltage.
- Potential divider: Two series resistors that split the supply voltage into a smaller output voltage.
- Equivalent resistance: The single resistance that replaces a network and draws the same current from the supply.
- Loading effect: The reduction in output voltage when a load draws current from a potential divider.
- Potentiometer: A variable resistor with a sliding contact used as an adjustable potential divider.
❓ Practice Questions
Q: Three resistors of 2 Ω, 3 Ω and 5 Ω are connected in series. What is the total resistance?
Q: Two resistors of 6 Ω and 3 Ω are connected in parallel. What is the total resistance?
Q: A 12 V supply feeds a potential divider with R1 = 4 kΩ and R2 = 8 kΩ. What is V_out?
Q: Why does connecting a load across a potential divider reduce V_out?
Q: In a series circuit of 10 Ω and 20 Ω with a 9 V supply, what is the voltage across the 20 Ω resistor?
✅ Answers
- R_total = 2 + 3 + 5 = 10 Ω.
- R_total = (6 × 3)/(6 + 3) = 18/9 = 2 Ω.
- V_out = 12 × 8/(4 + 8) = 12 × 8/12 = 8 V.
- The load is in parallel with R2, lowering the effective resistance of the lower branch and reducing the voltage fraction across it.
- V = 9 × 20/(10 + 20) = 9 × 20/30 = 6 V.
🎯 Exam Tips
- Always draw the circuit and label it before attempting calculations.
- For mixed networks, simplify parallel sections first, then add series resistances.
- State the formula for a potential divider before substituting values.
- Show that the sum of voltages across series resistors equals the supply voltage as a check.
- Remember that a loaded potential divider will have a lower output than the unloaded calculation predicts.
📝 Exam Technique
GCSE Electronics Exam Tips — Ohm's Law & Resistor Networks:
1. For Ohm's Law & Resistor Networks questions, use correct electronic symbols and terminology
2. Always show your working in calculations, including units at each step
3. When analysing circuits, state which law or rule you are applying first
4. For evaluation questions on Ohm's Law & Resistor Networks, compare component choices and consider cost, reliability and tolerance
5. Draw circuit diagrams neatly with conventional symbols
1. For Ohm's Law & Resistor Networks questions, use correct electronic symbols and terminology
2. Always show your working in calculations, including units at each step
3. When analysing circuits, state which law or rule you are applying first
4. For evaluation questions on Ohm's Law & Resistor Networks, compare component choices and consider cost, reliability and tolerance
5. Draw circuit diagrams neatly with conventional symbols
⚠️ Common Errors
✗ Adding resistances directly for a parallel combination. ✓ Use 1/R_total = 1/R1 + 1/R2 for parallel; add directly only for series.
✗ Using R_total = R1 + R2 when resistors are in parallel. ✓ For two parallel resistors, use R_total = (R1 × R2)/(R1 + R2).
✗ Forgetting to account for loading when a potential divider drives another circuit. ✓ Recalculate the lower branch as R2 in parallel with the load resistance.
✗ Assuming current splits equally in parallel branches. ✓ Current splits inversely proportional to branch resistance.
✍️ Model Answer
Full-Mark Response
Explain how to calculate the total resistance of a mixed series-parallel resistor network, and describe how a potential divider works.
To calculate total resistance of a mixed network, first identify which resistors are in parallel and combine them using 1/R_total = 1/R1 + 1/R2 + …, then add any series resistances to get the overall equivalent resistance. A potential divider consists of two resistors (R1 and R2) in series across a supply voltage. The output voltage taken across R2 is V_out = V_in × R2/(R1 + R2). The voltage divides in proportion to the resistances: the larger R2 is relative to R1, the greater the output voltage. If a load is connected across R2, it forms a parallel combination with R2, reducing the effective lower resistance and therefore reducing V_out. This loading effect must be considered in practical circuits.
📊 AO Deep Dive
Assessment Objective Analysis
AO1 (Knowledge & Understanding): Demonstrate knowledge and understanding of ohm's law & resistor networks, including electronic components, circuit theory and systems concepts relevant to WJEC Eduqas C690QS.
AO2 (Application): Apply knowledge and understanding of ohm's law & resistor networks to analyse, design and construct electronic circuits and systems.
AO3 (Evaluation): Evaluate electronic circuits and systems, making reasoned judgements about design choices, performance and practical considerations, constructing supported arguments.
📝 Exam Questions by Topic
🎬 Video Resources
Ready to ace your GCSE Electronics exams?
Get the best revision books and guides to boost your grades.