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6.3 Kirchhoff’s Laws
Resistance in Series
The total resistance of a number of resistors connected in series is simply the sum of
the individual resistors. The equivalent resistance, Rs, can be determined from:
Rs = R1 + R2 + R3 + …. + Rn
In a series circuit the current is the same through out the circuit.
Using Ohm’s law: R = V/I:
Vs
=
V1
+
V2
+
V3
+…+
Vn
I
I
I
I
I
And if current, I, is the same through out the circuit the voltage across the emf source VAB
could be determined by:
VAB = V1 + V2 + V3 + …. + Vn
p. 241 - 242
6.3 Kirchhoff’s Laws
Resistance in Parallel
A parallel circuit contains more than one pathway or branch for
the electrons travel through as they make their way through the
circuit.
The current first splits at junction point C, to travel through one
of 3 branches and then rejoins at junction point D.
There is a conservation of electrons going on here. The total current at junction point C
split part would equal the total current reformed at junction point D.
At a junction point, Current in = Current out and could be written as:
Io = I1 + I2 + I3 + …. + In
p. 242
6.3 Kirchhoff’s Laws
Resistance in Parallel (con’t)
The potential difference or voltage across the branches of a parallel
circuit is same.
VAB = V1 = V2 = V3 = …. = Vn
Where V1, V2 , &V3 is the potential difference across resistors R1,
R2, & R3.
Using Ohm’s Law I = V/R, and knowing that the potential difference is the same in a
parallel circuit the equivalent resistance in a parallel circuit can be determined by:
1
Rp
=
1
1
+
R1
R2
+
1
R3
+…+
1
Rn
p. 242 - 243
6.3 Kirchhoff’s Laws
Combined Series and Parallel Circuits:
Most circuits in real life have both series parts and parallel parts with in the same circuit
as shown below:
The rules for series and parallel circuits have
to be applied in a logical manner to solve for
the equivalent resistance for this circuit. The
first step is to reduce the parallel resistors to
an equivalent series resistance and then treat
the rest of the circuit as being a series circuit.
See Sample problem 6.3.1 on p. 244 for an example of how to do this.
p. 244
6.3 Kirchhoff’s Laws
Kirchhoff’s Laws for Electric Circuits
The rules that we have been examining can be summarized as follows:
Kirchhoff’s Current Rule
At any junction point in a circuit the sum of all the current entering that
junction point equals the sum of all the currents leaving that junction point
Kirchhoff’s Voltage rule
The algebraic sum of all the changes in potential around closed path a circuit is
zero.
p. 246
6.3 Kirchhoff’s Laws
Key Questions
In this section, you should understand how to solve the following key questions.
Page 245 – Practice Problems 6.3.1 #2
Page 246 - 247 – Quick Check #3 & 4
Page 251 – 253 – Review 6.2 #1,3,5,7, & 9