4.2.2 Series and Parallel Circuits

In GCSE Physics, you must be able to distinguish between the two main ways of connecting electrical components: series and parallel. The behavior of current, potential difference, and resistance changes significantly depending on the circuit type.

1. Series Circuits

In a series circuit, all components are connected one after another in a single loop. If one component breaks (e.g., a bulb blows), the entire circuit is broken and current stops flowing.

Rules for Series Circuits:

1. Current ($I$): The current is the same through each component. I_{total} = I_1 = I_2 = ...
2. Potential Difference ($V$): The total potential difference of the power supply is shared between the components. $V_{total}=V_1+V_2+...$
3. Resistance ($R$): The total resistance of two or more components is the sum of the resistance of each component. $R_{total}=R_1+R_2+...$

Key Concept: Adding more resistors in series increases the total resistance (in Ohms, $\Omega$ ). This is because the charge has to pass through more "obstacles," which reduces the total current.

2. Parallel Circuits

In a parallel circuit, there are multiple branches (loops). If one branch is broken, current can still flow through the others. This is why lights in your home are wired in parallel.

Rules for Parallel Circuits:

1. Current (I): The total current through the whole circuit is the sum of the currents through the separate branches. $I_{total}=I_1+I_2+...$
2. Potential Difference ($V$): The potential difference across each branch is the same.$V_1=V_2=V_{source}$
3. Resistance ($R$): The total resistance of two resistors in parallel is less than the resistance of the smallest individual resistor.

Edge Case: Why does adding resistors in parallel decrease resistance? Imagine a busy checkout at a supermarket. If you open a second "branch" (lane), it is easier for the "charge" (customers) to flow, even if the new lane has its own resistance.

3. Summary Table: Comparison of Rules

4. Mathematical Example: Mixed Rules

Question: Two resistors, $R_1=4\Omega$ and $R_2=6\Omega$ , are connected in series to a 20V battery.

1. Calculate the total resistance.
2. Calculate the total current in the circuit.

Step 1: Calculate Total Resistance ($R_{total}$)

In series, we simply add them:

$R_{total}=4\Omega +6\Omega =10\Omega$

Step 2: Calculate Current ($I$) using Ohm's Law

Using V = I * R:

$I=\frac{V}{R}$

$I=\frac{20V}{10\Omega }=2A$

Answer: The total resistance is $10\Omega$ and the current is $2A$.

5. Exam Tip: Cells in Series

When multiple cells are connected in series, provided they are all connected in the same direction, their total potential difference is the sum of their individual voltages.

$V_{total}=V_{cell1}+V_{cell2}+...$

If a cell is facing the "wrong" way, its potential difference is subtracted from the total.