Battery

#raw Batteries are devices capable of producing a Voltage between their ends (terminals) through the use of chemical reactions. They are used in circuits as a reliable source power, but come with drawbacks due to the chemical reactions and properties of materials used to make them.

Chemical Reactions §

In reality, a battery is made up of several electrochemical cells, which convert Electrical Potential Energy to chemical energy, and in the case of rechargeable batteries, vice versa. When these electrochemical cells are connected together, either in series or in parallel, they create a battery.

The most common electrochemical cell is the galvanic (also called voltaic) cell.

#todo Maybe someday, when I study more chemistry.

Voltage & Internal Resistance §

Batteries are real EMF sources, which means that the electrons within the battery have to fight against the electric field created by them in the first place to leave a circuit. This is defined as the internal resistance of the battery:

The Electrical Potential difference (voltage) in a battery can be determined using a circuit:

$$\mathcal{E}=I{R}_{int}+I{R}_{load}=V_{battery}+V_{load}$$

Over time, $V_{battery}$ decreases as the electrodes used for the chemical reactions degrade, which increases $V_{int}$.

Within device §

$$EMF=\frac{dW}{dq}$$

An ideal emf has no internal resistance A real emf device has some internal resistance.

$V_{batt}=V_{internal}+V_{load}$

In a charge $dq$ going through $dt$, with an electric potential $V$. We have potential electric energy:

$dU=\text{d}qV$ $I=\frac{dq}{dt}$ $dU=IVdt$

$$Power,P=\frac{dU}{dt}=IV$$

Drude Model of Conduction shows power is dissipated mainly through heat, as electrons inside device collide with the material, transferring kinetic energy to the lattice which is converted to thermal energy, heating up the material.

Units: $W$