d.c. Circuits
Kirchhoff'’s Rules
There are two basic principles of circuitry that can be used to analyze most electrical circuits. They are called
Kirchhoff’s rules.
1.
Kirchhoff’s Junction rule (or current rule): The sum of the currents entering any circuit junction is equal to the sum
of the currents leaving the junction. For example, if we apply the rule to the circuit in Figure 1 at the junction
labeled as B, we get:
I
1
= I
2
+ I
3
2.
Kirchhoff’s Loop rule: The sum of the changes in potential across all elements around any closed circuit loop is
equal to zero, with the conventions that traversing an emf from () to (+) results in a positive potential change and
resistors traversed in the direction of the current result in a negative potential change. For example, if we apply
the rule to the circuit in Figure 1, taking the loop starting at point A and going clockwise through B, C, D and back
to A, we get:
 I
1
R
1
– I
3
R
3
– I
4
R
4
+ E
2
+ E
1
= 0
The first rule is a consequence of the
conservation of charge.
In a circuit,
electrons cannot be created nor destroyed.
If a current comes to a juncture, the total
amount of electrons going into the juncture
must be equal to the total number of
electrons leaving the juncture.
The second is a consequence of the law of
conservation of energy. We have learned
when dealing with gravity, that if a hiking
path leads you back to the original starting
point there is no net change in gravitational
potential energy. Similarly in a circuit, a
path that leads back to the starting point results in no in change in electrical potential energy.
To easily apply Kirchhoff’s rules, it might be beneficial to label and mark currents for each of the circuit branches. You
then calculate the voltage drop across each of the devices and mark which side of the device, according the current
direction chosen, is at the higher electrical potential. All labels were added in red in Figure 1.
Use of Meters Reminder
We usually use an Ammeter to measure current and a
Voltmeter to measure voltage. When drawing a schematic of a
circuit, we usually label the Ammeter as “A” and the voltmeter
with “V”. An example schematic is shown in Figure 2. Along
with the ammeter and the voltmeter, the schematic includes 4
other devices: a power supply designated by E, and three
resistors designated by R.
When measuring current with an ammeter, the ammeter should
be placed in series with the device we want to measure the
current through. For example, as shown in the Figure, if we want to measure the current through R
1
, we place the
ammeter in series with R
1
. The same current should flow through both R
1
and the ammeter.
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 Summer '10
 Adler
 Physics, Current, Electrical Circuits, SEPTA Regional Rail, power supply, ... ..., Kirchhoff

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