# What does electric potential mean in a circuit?

As we know that electric potential at a point is defined as a work done by me to carry unit charge from infinity to that point. How can I use this definition in an electric circuit that contains a battery? Suppose electric potential at a point in a circuit is 4 volt. What does this means? l. Is it means that work done by me to carry unit charge from infinity to that point in a circuit is 4 Joules?

When we talk about a potential we actually always mean a potential difference i.e. the difference from the potential at some convenient reference point. That's because we can only ever measure potential differences and not absolute values. So when you say:

electric potential at a point is defined as a work done by me to carry unit charge from infinity to that point

What this actually means is that the potential difference between infinity and some point $\mathbf r$ is the work done per unit charge to move a charge from infinity to that point.

Now suppose we have a battery with a potential $V$. What we mean by this is that to transport a unit charge from the cathode to the anode inside the battery takes an amount of work equal to $V$ i.e. $V$ is the potential difference between the terminals of the battery.

When we put the battery in a circuit we normally take the anode to be our zero point for the potential. So when we say the voltage at some point in the circuit is $V$ we mean that the potential difference between the anode and the point is $V$.

Suppose electric potential at a point in a circuit is 4 volt.

An electric circuit has two or more nodes which is essentially where two or more circuit elements connect. For example, a circuit consisting of a battery and a resistor has two nodes; one where the more positive battery terminal connects to one terminal of the resistor, and the other where the more negative battery terminal connects to the remaining terminal of the resistor.

In this context, we talk about the the voltage across a circuit element, e.g., the voltage across the battery, the voltage across the resistor, etc.

What we mean by voltage across is the potential difference between the terminals of the circuit element.

In more complicated circuits with more than two nodes, it is often the case that we choose one node as the reference (ground, datum) node. Then the node voltage (voltage at a node or point in a circuit) is understood to be the potential difference between that node and the reference node.

Physically, picture this as fixing the black lead of your voltmeter to the reference node and then placing the red lead on any other node in the circuit. The voltage read from the voltmeter is then the voltage at that node, the node voltage.

Clearly, the voltage at the reference node is $0\,\mathrm{V}$ since placing the red lead at the same point as the black lead will (ideally) give a $0\,\mathrm{V}$ reading.

• Is it necessary to to take -ve electrode as 0volt in the battery – Keshav Dec 23 '17 at 14:01
• @Keshav, necessary for what? – Alfred Centauri Dec 23 '17 at 15:45

In EM-Fields we take infinity to be the zero reference In Batteries and Circuits, we take the cathode as the zero reference

So the Voltage in more generic terms can be defined as the work done by an external force to transfer a unit charge from zero reference to the given point.