Introductory Physics Volume Two

3.6 Resistors in Combination 63
parallel. The diagram below will help explain why these configurations
are named in this way.
Suppose that we have two resistors in series. Since they are in
series they must carry the same current.
I 1 = I 2 = I
We also know that the potential difference across the pair is the sum
of the potential differences across each individual resistor;
∆V = ∆V 1 + ∆V 2
= I 1 R 1 + I 2 R 2
= IR 1 + IR 2
= I(R 1 + R 2 )
−→ R effective = R 1 + R 2
We see that the pair of resistors in series still follow Ohm’s law, and
that the pair act as a single resistor with an effective resistance of
R effective = R 1 + R 2 .
Series Resistors
Parallel Resistors
+
–
ΔV
+
ΔV 1
–
+
ΔV 2
–
I 1
I 2
Now consider two resistors in parallel. Since they are in parallel
the must have the same electric potential.
∆V 1 = ∆V 2 = ∆V
We also know from the junction rule that the net current going into the
system is equal to the sum of the two currents going into the resistors.
I = I 1 + I 2 = ∆V 1
+ ∆V 2
R 1 R
[ 2
1
= ∆V + 1 ]
R 1 R 2
= ∆V
R 1
I
+ ∆V
R 2
−→
1
R effective
= 1 R 1
+ 1 R 2