What Happens Atomically When Batteries Are Connected in Series?

Connecting batteries in series does not combine their atoms or make electrons move faster by itself. Instead, each battery contributes a chemical energy source. When the batteries are oriented so that their emfs reinforce, a unit of charge can gain energy from both sources in succession, making the total potential difference approximately the sum of their voltages.

What “series” means

For two batteries to add their voltages, connect the positive terminal of one to the negative terminal of the other. The two unconnected outer terminals become the combined supply terminals. This is an aiding series connection.

For ideal sources, the total electromotive force (emf) is

$$\mathcal{E}_{\text{total}}=\mathcal{E}_1+\mathcal{E}_2.$$

Emf is energy supplied per unit charge, measured in volts: $1\text{ V}=1\text{ J/C}$. It is not a force in the mechanical sense. If one cell has an emf of $1.5\text{ V}$ and another also has an emf of $1.5\text{ V}$, their aiding series combination has an ideal emf of $3.0\text{ V}$.

If one battery is reversed, the emfs oppose instead. The net emf is then the difference in magnitudes, with its direction set by the larger source. Connecting real, unequal batteries in opposition can cause unwanted current, so do not do this unless the circuit is designed for it.

What happens inside a battery

A battery converts chemical energy into electrical energy through reactions at its electrodes. During discharge, oxidation at the negative electrode releases electrons into the external metal circuit, while reduction at the positive electrode consumes electrons arriving through that circuit. The electrolyte and other internal materials support the corresponding ionic processes and help complete the electrochemical reaction.

These reactions maintain a separation of charge and an electrochemical potential difference between the terminals. The battery’s chemistry effectively does work to move charge in a direction that the electric field alone would not drive it. This is why a battery can keep supplying energy to a circuit rather than behaving like a one-time store of separated charge.

In a typical battery, electrons travel through the external wires and components; ions carry charge through the electrolyte. The details of the reactions and mobile ions depend on the battery chemistry, but the central energy accounting is the same.

Why the voltages add

Imagine a charge going around a complete circuit that contains both cells. As it passes through each source from that cell’s negative terminal to its positive terminal, the source supplies energy. For a positive charge amount $q$, the energy supplied by cell $i$ is $q\mathcal{E}_i$. In an aiding series connection, the contributions add:

$$\Delta U_{\text{source}}=q\mathcal{E}_1+q\mathcal{E}_2 =q(\mathcal{E}_1+\mathcal{E}_2).$$

Dividing by the charge gives the combined emf. The same idea applies to electrons: the magnitude of the energy transferred per electron across a potential difference of $V$ volts is $eV$, where $e$ is the elementary charge. The electron’s charge is negative, so the sign of its change in electric potential energy depends on its direction of travel. The battery’s chemistry supplies the energy that is delivered to the circuit.

The connection between the cells also has a physical role. In the brief transient after connection, small amounts of charge redistribute on the terminals and wires. That redistribution establishes the electric fields and node potentials appropriate to the connected circuit. Once steady conditions are reached, the cells’ chemical reactions maintain their respective terminal differences, and a load connected across the two outer terminals experiences the combined voltage.

Worked example: two 1.5 V cells

Take two cells, each with an emf of $1.5\text{ V}$, and join the positive terminal of the first to the negative terminal of the second. The remaining terminals provide the output. The ideal total emf is

$$\mathcal{E}_{\text{total}}=1.5\text{ V}+1.5\text{ V}=3.0\text{ V}.$$

A charge of $1\text{ C}$ moving around the circuit receives $1.5\text{ J}$ of energy from each cell, or $3.0\text{ J}$ in total, before losses in the cells and wires. This energy is then transferred to circuit components such as a lamp or resistor.

Real batteries have internal resistance. If each cell has internal resistance $0.20\,\Omega$ and the circuit draws $0.10\text{ A}$, the combined internal voltage loss is

$$I(r_1+r_2)=0.10\text{ A}(0.20\,\Omega+0.20\,\Omega)=0.04\text{ V}.$$

The terminal voltage under this load is therefore about $3.00-0.04=2.96\text{ V}$, assuming the cells have the stated emfs and resistances. With no load, a voltmeter with very high input resistance would read close to the combined emf.

Common misconceptions

• Voltage is not a count of electrons. Two cells in series do not double the number of electrons in the wire. They increase the energy available per unit charge.
• The electrons do not have to cross the electrolyte. In ordinary cells, electrons move through external conductors; ions and chemical reactions carry the process internally.
• The voltage does not guarantee a particular current. Current also depends on the connected load and the batteries’ internal resistance. A higher series voltage can drive more current through the same load, but the actual current is determined by the whole circuit.
• The cells must be oriented correctly. Their emfs add only when the connection makes them act in the same direction around the circuit.

Series connection increases the supply voltage, but it does not create energy from nothing: the cells’ chemical energy is converted into electrical energy as they discharge.