The junction rule deals with “junctions,” where a circuit splits into more than one branch,
or when several branches reunite to form a single wire. The rule states:
The current coming into a junction equals the current coming out.
This rule comes from the conservation of charge: the charge per unit time going into the
junction must equal the charge per unit time coming out. In other words, when a circuit
separates into more than one branch—as with resistors in parallel—then the total current
is split between the different branches.
The junction rule tells us how to deal with resistors in series and other cases of circuits
branching in two or more directions. If we encounter three resistors in series, we know
that the sum of the current through all three resistors is equal to the current in the wire
before it divides into three parallel branches.
Let’s apply the junction rule to the junction at B in the diagram we looked at earlier.
According to the arrows we’ve drawn, the current in the diagram flows from A into B
across and flows out of B in two branches: one across toward E and the other
toward C. According to the junction rule, the current flowing into B must equal the
current flowing out of B. If we label the current going into B as and the current going
out of B toward E as , we can conclude that the current going out of B toward C is –
. That way, the current flowing into B is and the current flowing out of B is + ( –
) =.The Loop Rule
The loop rule addresses the voltage drop of any closed loop in the circuit. It states:
The sum of the voltage drops around a closed loop is zero.
This is actually a statement of conservation of energy: every increase in potential energy,
such as from a battery, must be balanced by a decrease, such as across a resistor. In other
words, the voltage drop across all the resistors in a closed loop is equal to the voltage of
the batteries in that loop.
In a normal circuit, we know that when the current crosses a resistor, R, the voltage drops
by IR, and when the current crosses a battery, V, the voltage rises by V. When we trace a
loop—we can choose to do so in the clockwise direction or the counterclockwise direction
—we may sometimes find ourselves tracing the loop against the direction of the arrows