1. Combinational Resistance Networks
This type of circuit requires the use of both series and parallel circuit
analysis.
The total current (IT ) flowing through R1 splits up in the branch currents of the
parallel section.
It is good practice to redraw the circuit as a series circuit once the parallel
sections have been determined.
IT =
E
Reff
Reff = R1 + RP
RP R2 R3
1 1 1
= +
=E
+
-
IT
R3R2
R1
I1 I2
IT
RP
E
+
-
IT
IT
R1

2. Combinational Resistance Networks
Activity 1
1. Determine the effective resistance when a parallel circuit comprising a 50Ω
and 25Ω is connected in series with a 10Ω resistance.
2. A circuit comprising two resistances in parallel (10Ω, 20Ω) has a 50Ω
resistance connected on one side and a 20Ω resistance connected on the
other side. Determine a) the effective resistance.
3. Determine the effective resistance when two resistances (5Ω and 15Ω) are
connected in series and a third resistance (40Ω) is connected in parallel
with this combination.
Sketch these circuits before starting to calculate your results.

3. Branch Current
The first stage is to determine the potential developed across the parallel
section (VRP). This voltage is then used to establish the current flowing in
the parallel branches, (IR2 & IR3).
The total current (IT ) flowing through R1 splits up in the branch currents of the
parallel section.
=E
+
-
IT
R3R2
R1
IR2 IR3
IT
RP
E
+
-
IT
IT
R1
VRP
IT =
E
Reff
VRP = IT RP IR2 =
VRP
R2
IR3 =
VRP
R3
IT = IR1 + IR2

4. Combinational Resistance Networks
Activity 1
1. Determine the effective resistance when a parallel circuit comprising a 50Ω
and 25Ω is connected in series with a 10Ω resistance. If the circuit is
connected to a 10 volt supply determine the current flowing in each branch
and the total current drawn from the supply.
2. A circuit comprising three resistances in parallel (10Ω, 5Ω, 20Ω) is
connected has a 30Ω resistance connected on one side and a 20Ω
resistance connected on the other side. If this combination is connected to
a 100v dc supply determine a) the effective resistance, b) the total current
flowing and c) the current in each of the parallel branches.
3. Two resistances (10Ω and 15Ω) are connected in series and a third
resistance (50Ω) is connected in parallel with this combination. The
complete circuit is connected to a 25 volt supply determine a) the current
flowing in each branch and hence the total current.
Sketch these circuits before starting to calculate your results.