4.3.2 Series and Parallel Circuits Revision Notes

1. Overview

Electrical components can be connected in two ways: series or parallel. Understanding how current, voltage (p.d.), and resistance behave in these arrangements is essential for designing circuits, from simple flashlights to complex household wiring.

Key Definitions

• Series Circuit: A circuit where components are connected one after another in a single loop.
• Parallel Circuit: A circuit where components are connected on separate branches, providing multiple paths for the current.
• Junction: A point in a parallel circuit where the circuit divides or combines.
• e.m.f. (Electromotive Force): The total energy supplied by a source (like a battery) to the electrical charge.
• Potential Difference (p.d.): The energy transferred per unit charge between two points in a circuit.

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Core Content

Current in Series

In a series circuit, there is only one path for the electrons to flow. Therefore, the current is the same at every point in the circuit.

• If an ammeter reads 2A near the battery, it will read 2A anywhere else in that loop.

Constructing Circuits

• Series: Connect components end-to-end. If one component breaks, the whole circuit stops working.
• Parallel: Connect components across each other. If one branch breaks, the others continue to function.
• 📊A simple series circuit with one battery and two lamps in a single loop vs. a parallel circuit with one battery and two lamps on separate branches.

Combined e.m.f. of Sources in Series

When multiple cells are connected in series (facing the same direction), their total e.m.f. is the sum of their individual e.m.f.s.

• Worked Example: Three 1.5V cells are connected in series.
  • Total e.m.f. = $1.5V + 1.5V + 1.5V = 4.5V$.

Combined Resistance in Series

The total resistance ($R_{Total}$) is the sum of all individual resistors.

• Formula: $R_{Total} = R_1 + R_2 + ...$
• Worked Example: A $5\Omega$ resistor and a $10\Omega$ resistor are in series.
  • $R_{Total} = 5 + 10 = 15\Omega$.

Current in Parallel

• The current from the source (the "main" part of the circuit) is always larger than the current in each individual branch.
• The total current is shared between the branches.

Combined Resistance in Parallel

• When resistors are connected in parallel, the total resistance is less than the resistance of the smallest individual resistor.
• This happens because you are providing more "paths" for the current to flow through.

Advantages of Parallel Circuits for Lighting

1. Independent Control: Each lamp can be switched on or off independently.
2. Constant Voltage: Every lamp receives the full voltage of the source, so they all shine brightly.
3. Reliability: If one lamp blows, the rest of the circuit stays closed and the other lamps remain lit.

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Extended Content (Extended Only)

Conservation of Charge at Junctions

Current is the flow of electrons. Because charge cannot be created or destroyed, the sum of currents entering a junction must equal the sum of currents leaving it.

• If 5A enters a junction and splits into two branches, and one branch has 2A, the other must have 3A ($5 - 2 = 3$).

Potential Difference in Series

The total p.d. supplied by the source is shared between the components.

• $V_{Source} = V_1 + V_2 + ...$
• Worked Example: A 12V battery is connected to two identical resistors in series. Each resistor will have a p.d. of 6V.

Potential Difference in Parallel

The p.d. across each branch in a parallel arrangement is the same as the p.d. across the whole arrangement.

• If a 9V battery is connected to three parallel branches, each branch has exactly 9V across it.

Calculating Parallel Resistance

For two resistors in parallel, use the reciprocal formula: $$\frac{1}{R_{Total}} = \frac{1}{R_1} + \frac{1}{R_2}$$

• Worked Example: Calculate the resistance of a $4\Omega$ and $6\Omega$ resistor in parallel.
  1. $\frac{1}{R_{Total}} = \frac{1}{4} + \frac{1}{6}$
  2. $\frac{1}{R_{Total}} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$
  3. $R_{Total} = \frac{12}{5} = 2.4\Omega$

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Key Equations

Equation	Symbols	Units
$R_s = R_1 + R_2$	$R$: Resistance	Ohms ($\Omega$)
$\frac{1}{R_p} = \frac{1}{R_1} + \frac{1}{R_2}$	$R$: Resistance	Ohms ($\Omega$)
$I_{in} = I_{out}$	$I$: Current	Amperes (A)
$V_{total} = V_1 + V_2$ (Series)	$V$: Potential Difference	Volts (V)

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Common Mistakes to Avoid

• ❌ Wrong: Thinking current is "used up" as it goes around a circuit.
• ✓ Right: Current is the same at all points in a series circuit; energy (p.d.) is what is transferred.
• ❌ Wrong: Thinking adding a resistor in parallel increases the total resistance.
• ✓ Right: Adding a parallel resistor decreases total resistance because you are adding a new path for the current.
• ❌ Wrong: Forgetting to "flip" the fraction at the end of a parallel resistance calculation.
• ✓ Right: Always calculate $1 \div (\text{your answer})$ to get $R_{Total}$.
• ❌ Wrong: Assuming the current in a branch can be higher than the total supply current.
• ✓ Right: The supply current is always the sum of all branch currents.

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Exam Tips

1. The "Smaller than Smallest" Check: After calculating parallel resistance, always check if your answer is smaller than the lowest value resistor in that arrangement. If it isn't, you've made a calculation error.
2. Identify Junctions: When looking at a complex diagram, circle the junctions. This helps you identify which components are in parallel and where the current will split.
3. Follow the Path: To check if components are in series, trace the path from the battery. If your finger never has to choose between two paths, those components are in series.