What's a loop current?

I just started mesh analysis, but don't really understand the concept of a loop current. The current in different parts of a loop is not necessarily constant - two parts of the same loop can have different currents. So how can you define one current for the whole loop?

• Does your textbook or lecture notes actually say there is only one current defined for the whole loop? Commented Mar 20, 2014 at 4:10
• Step back far enough, and all currents are loop currents. Commented Dec 17, 2017 at 13:18

The idea of a loop current is that for each loop you can identify in the mesh, you can find one value of current "attributable" just to that loop, and which passes through every leg of that loop.

Any leg (edge) of the mesh may be involved in more than one loop, in which case the actual current in that leg is the sum of the loop currents of those multiple loops.

It's like the flip side of the more intuitive observation that currents flowing into and out of a single node add to zero. (All current flowing in must flow out -- current can't just appear or disappear.)

• How do we know that the actual current can be broken down into loop currents?
– dfg
Commented Mar 20, 2014 at 14:26
• At least one way to reason about it is, as mentioned, that the sum of currents flowing into each node (with negative for the out direction) equals zero. This starting point is, I hope, intuitively sensible. From there, create equations for the current in the legs, solve, and you end up with the corresponding conclusion regarding loops. That describes "how it is known", not sure if it succeeds in convincing you :-). Commented Mar 20, 2014 at 23:49

The actual loop current is the summation of currents, and you can also have influence of currents from a nearby mesh. So If there is a shared branch between two meshes, say a resistor, then I_R = I1 + I2 , where I1 and I2 are the individual loop currents, which may be positive or negative, and probably produced by a current source or generated by a voltage source over a resistance.

• How do we know that the actual current can be broken down into loop currents?
– dfg
Commented Mar 20, 2014 at 14:45
• current exists as the flow of charge through actual components, and in real life through parasitic features of PCB traces etc. If you have a potential (voltage) and it is different between two areas(or nodes, usually called), there WILL be a flow of current - which is dictated by the path resistance, and/or inductance (parasitic or an actual discrete component). So basically, if you have a resistor or something with equivalent resistance (in a DC system) between two voltage levels (like, 5+V and 0V) then the current flowing down that path is/must be I = V/R. Commented Mar 21, 2014 at 0:16
• I get that there will be a current, but that doesn't mean that the current's can necessarily be broken down into loop currents does it?
– dfg
Commented Mar 21, 2014 at 0:49
• loop currents are just a theory they teach you for circuit analysis. The "loop" currents are only relevant if nearby circuits such as resistor networks, or multiple nearby power sources are interacting in some way. Maybe you have two contending constant current sources, acting in opposite directions, you could calculate the current through a 'branch' with a resistor on it, and therefore the node voltage/power loss of the resistor. What exactly do you mean by currents cant be broken down into loop currents? They can if there are multiple sources! That is the main point of learning the topic Commented Mar 21, 2014 at 1:46

In a circuit, with only linear elements in it, the current in any branch can be written as the linear combination$^{\dagger}$ of L currents. Where 'L' is the no. of loops in the circuit. These L currents are called loop currents.

It doesn't mean that all branches in a loop should have same current. It just means that the current through any branch in a loop can be expressed as the sum or difference of the corresponding loop current and neighboring loop current.

OR as you said, any branch current can be 'broken down' into loop currents.

$\small{ ^{\dagger} \text{linear combination with coefficients}\in \{0,1,-1\} }$

Bottom line - loop "current" is a mathematical construct used in KVL equations. It is only directly measurable in a loop with an unshared branch.