Comparing Series & Parallel Circuits

Circuit Types

Series circuits have components connected end-to-end in a single path. The current flows through each component one after another. If one component breaks, the whole circuit stops working.

Parallel circuits have components connected across separate branches. Each component is connected directly to the power supply, so the current can split and flow through multiple paths. If one component breaks, the others can still work.

Current in Circuits

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

In a parallel circuit, the current divides at junctions. The total current from the power supply is shared between the different branches. The current in each branch depends on the resistance of that branch.

Because parallel circuits provide multiple paths, the total current drawn from the power supply is higher than in a series circuit with the same components.

For instance, if a parallel circuit has two branches with currents of 2 A and 3 A, the total current supplied by the battery is:

$\text{Total current} = 2\,\text{A} + 3\,\text{A} = 5\,\text{A}$

Example: If a parallel circuit has three branches with currents 1 A, 2 A and 4 A, what is the total current supplied by the battery?

Using addition, total current $= 1 + 2 + 4 = 7\,\text{A}$.

Potential Difference

In a series circuit, the total potential difference (voltage) from the power supply is shared between the components. This means the voltage across each component adds up to the total voltage.

In a parallel circuit, the potential difference across each branch is the same and equal to the voltage of the power supply.

Voltmeters are connected in parallel across components to measure the potential difference. This is because they need to measure the voltage drop across a specific component without changing the current in the circuit. For example, a voltmeter connected across a resistor measures the voltage drop across that resistor.

For example, if a 12 V battery powers two resistors in series, and the voltage across one resistor is 7 V, the voltage across the other resistor must be:

$\text{Voltage across second resistor} = 12\,\text{V} - 7\,\text{V} = 5\,\text{V}$

Resistance in Circuits

In a series circuit, the total resistance is the sum of the individual resistances:

$$R_\text{total} = R_1 + R_2 + R_3 + \dots$$

Adding more resistors in series increases the total resistance, which reduces the total current flowing through the circuit.

In a parallel circuit, the total resistance decreases as more branches are added. This is because the current has more paths to flow through, reducing the overall resistance.

The total resistance in parallel is found using:

$$\frac{1}{R_\text{total}} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \dots$$

Lower total resistance in parallel circuits means a higher total current from the power supply compared to series circuits with the same components.

For example, two resistors of 4 $\Omega$ and 12 $\Omega$ in series have a total resistance of:

$$R_\text{total} = 4\,\Omega + 12\,\Omega = 16\,\Omega$$

The same resistors in parallel have a total resistance of:

$$\frac{1}{R_\text{total}} = \frac{1}{4} + \frac{1}{12} = \frac{3}{12} + \frac{1}{12} = \frac{4}{12} = \frac{1}{3}$$

So,

$$R_\text{total} = 3\,\Omega$$