Basic Concepts

        Charge usually flows through some sort of metallic wire, flowing through the atomic lattice.  Although it is physically unlike water flowing in a pipe, that analogy is sometimes drawn. Like water confined to the interior of a pipe, charge is confined to flow within a wire, and it doesn't leave the surface of the wire. You may want to think in those terms as you interpret current flow in the sketches and diagrams that follow.  We will be developing rules for current flow in circuits in this section.  You will need to know about that in order to be able to analyze larger circuits with lots of elements.

        In practice current flows in wires and often splits between two or more devices.  We need to consider what happens in networks of conductors in which current can split.  Single wires carrying current aren't the most important case we can look at, and you need to learn about Kirchhoff's Current Law which describes those situations where we have large networks of interconnected elements carrying current.  Those kinds of circuits will have many connection points (called nodes) where current can split into smaller currents.  Shown below is part of a circuit.  Current (I) comes in from the left and splits into two parts, I₁ and I₂.  There is one simple relationship between these two currents and the current, I, flowing in from the left below.

Here, a red dot has been placed over both of the nodes in the picture.

        Focus attention on a very short time, DT.  Assume all currents constant during DT.

• A current, I, flows into the top node, and I₁ and I₂ are flowing out of the node.  No charge accumulates!
• During time DT, the total amount of charge that flows into the node is zero so:
• IDT - I₁DT - I₂DT  = 0
• And during DT,
• IDT is the charge flowing in.
• I₁DT is the charge flowing through the left resistor.
• I₂DT is the charge flowing through the right resistor.
• So, we have - for the period of time DT, the total amount of charge that flows into the node is zero so:
• IDT - I₁DT - I₂DT  = 0
• Cancelling the DT's everywhere, we get:
• I - I₁ - I₂  = 0
• Which can be rephrased as:
• The sum of the currents flowing into the node is zero.
• or
• I  =  I₁ + I₂
• which says that "The current entering the node equals the current leaving the node."

• When we have the expression:
• I - I₁ - I₂  = 0
• Or when we think "The sum of the currents flowing into the node is zero."
• We interpret I as a current entering and - I₁ and  - I₂ also as currents entering.  Note the negative signs!
• Since I₁ is leaving the node, then we can think of  - I₁ as the value of the current entering.
• We do the same for I₂ and - I₂.

When we have the expression:

• I = I₁ + I₂  = 0
• Or when we think "The sum of the currents flowing into the node equals the sum of the currents leaving the node."

We interpret I as a current entering and I₁ and  I₂ as currents leaving.

3.  In this circuit - which you saw above - determine the current I₂, in terms of trhe other two currents.  You will need to write KCL at the node marked with a red dot.  Notice that we have defined current symbols and polarities for all the currents involved.

6.  Here's a problem for you.  In 10 seconds, an observer - Willy Nilly - notices that 35 coulombs of charge leaves node "n" in this circuit, heading for node "x".  (Vn is the voltage at node "n", etc.)  In the same ten seconds, 22 coulombs of charge leaves node "n" heading for node "z".  Determine the current, I_y.