Batteries in Series and in Parallel
Simple Explanation
Connecting batteries in series adds up their EMFs (giving a higher total voltage), while connecting identical batteries in parallel keeps the same EMF but reduces the total internal resistance, letting the combination supply more current.
Why Do We Need It?
This is exactly why multiple AA batteries are stacked in series inside a flashlight (for higher voltage), while large battery banks use parallel connections (for higher total current capacity) β the right choice depends on what the circuit actually needs.
See It
Two battery cell symbols connected end-to-end in a single line, their EMFs adding together
Formula
Batteries in Series and in Parallel
Series: Ξ΅_total = Ξ΅β+Ξ΅β+β¦, r_total = rβ+rβ+β¦; Parallel (identical cells): Ξ΅_total = Ξ΅, r_total = r/n
Connecting batteries in series adds up their EMFs (and internal resistances) to give a higher voltage; connecting identical batteries in parallel keeps the same EMF but reduces the effective internal resistance, letting more current be supplied.
- Ξ΅_total
- β total (equivalent) EMF of the combination, in volts (V)
- r_total
- β total (equivalent) internal resistance, in ohms (Ξ©)
- n
- β number of identical cells connected in parallel
When to use it: Whenever the total EMF and internal resistance of several batteries connected in series or parallel needs to be found.
Worked Example
Find the total EMF of cells in series
Three identical 1.5 V cells are connected in series. Find the total EMF.
Why Does This Work?
In series, the positive terminal of one cell connects to the negative terminal of the next, so each cell adds its own push to the charge moving through the circuit β the total energy given to each unit of charge is the sum of what every cell individually contributes. In parallel, identical cells share the current-supplying burden between them, effectively reducing the combined internal resistance.
Real-Life Example
Why a flashlight uses multiple AA batteries stacked in series
A flashlight typically uses two or more AA batteries stacked end-to-end (series), rather than side-by-side.
Stacking them in series adds their EMFs together (e.g. two 1.5 V cells give 3 V), providing enough voltage to properly light the bulb β a single 1.5 V cell alone often is not enough.
Practice
Two identical 1.5 V cells, each with internal resistance 0.2 Ξ©, are connected in PARALLEL. Find the total internal resistance.
MediumCommon mistake
Assuming parallel-connected cells add their EMFs like series cells do β identical cells in parallel keep the SAME EMF as a single cell; only their combined internal resistance (and current capacity) changes.
Quick Review
- Series: Ξ΅_total=Ξ΅β+Ξ΅β+β¦, r_total=rβ+rβ+β¦.
- Parallel (identical cells): Ξ΅_total=Ξ΅ (unchanged), r_total=r/n.
- Series for more voltage; parallel for more current capacity.