Voltage

Voltage is electric potential difference: the difference in Electric potential between two points.

$V_{ab}=V_a-V_b=\frac{W}{q}$

Read this as “joules per coulomb.” A $9\mathrm{V}$ battery can transfer about $9\mathrm{J}$ of energy to each coulomb of charge that passes through the external circuit, ignoring internal losses.

Voltage is relative. You can choose any node as $0\mathrm{V}$, just like choosing the origin on a graph. Shifting every node voltage by the same constant changes no currents, energies, or measurements. What matters is the difference between nodes.

In simple electronics, voltage across a Resistance and Current through it are related by Ohm’s law:

$V=IR$

Polarity matters. If current enters the positive-labelled side of a passive component, that component absorbs power:

$P=IV$

If current leaves the positive terminal, the device is delivering power, as an ideal battery does.

Common mistake: saying voltage “flows.” Charge flows; voltage is a difference in energy per charge between two points. Another trap is calling voltage the cause of current without mentioning the whole circuit path: an open circuit can have voltage but essentially no steady current.