Different types of bulbs or  
electrical devices can be  
Determine the current reading on the  
ammeter in the circuit shown on the diagram  
below.  
connected in parallel even if they  
require different currents, as long  
as the voltage is the same.  
Mixed resistors  
If more than two resistors are mixed in  
series and parallel connections in one  
circuit, to find the equivalent, we consider  
the connection with a greater number of  
resistors first.  
Consider the diagram below  
Solution  
Step 1: To calculate the resistance in parallel  
for the three resistors  
1
1
1
1
=
+
+
RT  
R1  
R2  
R3  
To find the total resistance, two steps must  
be followed  
1
1
1
1
=
+
+
RT  
24  
8
12  
Step 1: To calculate the total resistance in  
parallel  
1
1
=
RT  
4
1
1
1
=
+
RT = 4 Ω  
RP  
R1  
R2  
Step 2: To calculate the resistance in parallel  
for the three resistors  
Step 2: To calculate the total resistance in  
series  
1
1
1
1
RS = R3 + R4  
=
+
+
RT  
R4  
R5  
R6  
1
1
1
1
=
+
+
Step 3: To calculate resistance of the  
combined circuit in series  
RT  
6
3
6
1
2
3
=
RT = RP + RS  
RT  
RT = 1.5 Ω  
Step 3: To calculate the total resistance in  
series  
Example 01  
The new circuit now is a series connection,  
of 20Ω, 1.5Ω, 4Ω and 15Ω  
Step 3: To find the voltage across each  
wire  
RT = R1 + R2 + R3 + R4  
RT = 20Ω + 1.5Ω + 4Ω + 15Ω  
RT = 40.5 Ω  
Across the 6Ω wire alone 푉 = 퐼푅1  
1
푉 = 2 × 6  
1
Step 4: To find the total current, I  
푉 = 12푉  
1
V
I =  
R
Across the 4Ω wire alone 푉 = 퐼푅2  
2
9 V  
I =  
푉 = 2 × 4  
2
40.5 Ω  
푉 = 8푉  
2
I = 0.22 A  
Therefore, the current reading on the  
ammeter in the circuit is 0.22 A  
Example 03  
A circuit consists of a 1Ω wire in series with  
a parallel arrangement of 6Ω and 3Ω and a  
potential difference of 12V is connected  
across the whole circuit. Calculate the  
currents in each of the wires and the p.d  
across each.  
Example 02  
A resistance of 6Ω is in series with one of  
4Ω and a p.d of 20V is applied across the  
whole arrangement. Calculate the current in  
each wire and the p.d across each.  
Solution  
Consider the diagram below which shows  
the conditions for the problem  
Solution  
20V is the p.d across both wires together  
Step 1: To find the total resistance in  
the circuit  
Resistance in series = 푅1 + 푅2  
Resistance in series = 6Ω + 4Ω  
Resistance in series = 10Ω  
Solution  
Step 2: To find the total current in the  
circuit  
Since the 12V p.d is across the whole  
circuit, then we must first find the total  
resistance in the circuit.  
푣표푙푡푎푔푒  
푐푢푟푟푒푛푡 =  
푟푒푠푖푠푡푎푛푐푒  
Step1: To find the resistance of the  
parallel circuit of 6Ω and the 3Ω resistors  
20  
푐푢푟푟푒푛푡 =  
10  
1
1
1
=
+
푐푢푟푟푒푛푡 = 2퐴  
푅푝  
푅1  
푅2  
1
1
1
푐푢푟푟푒푛푡 = 1.33퐴  
=
+
푅푝  
6
3
Step 5: To find the current 푰ퟐ in the  
3Ω wire.  
푅푝 = 2Ω  
푣표푙푡푎푔푒  
푐푢푟푟푒푛푡 =  
Step2: To find the resistance of the series  
circuit between 2Ω and the 1Ω resistors  
푟푒푠푖푠푡푎푛푐푒  
8푉  
푐푢푟푟푒푛푡 =  
3Ω  
Resistance in series = 푅1 + 푅2  
Resistance in series = 2Ω + 1Ω  
Resistance in series = 3Ω  
푐푢푟푟푒푛푡 = 2.67퐴  
(c) Thus, the currents are respectively, 4A,  
1.33A and 2.67A  
Step 3: To find the total current in the  
circuit  
(d) The p.d.s are respectively, 4V, 8V and  
8V  
푣표푙푡푎푔푒  
푐푢푟푟푒푛푡 =  
푟푒푠푖푠푡푎푛푐푒  
Alternatively, the currents in the 6Ω and  
3Ω wires can be obtained as follows.  
12  
푐푢푟푟푒푛푡 =  
3
(a) Current in 6Ω wire  
푐푢푟푟푒푛푡 = 4퐴  
This is the current in the 1Ω because it flows  
from the 12V supply.  
3
퐼1 =  
× 4퐴  
3 + 6  
퐼1 = 1.33퐴  
Step 4: To find the current 푰ퟏ in the  
6Ω wire.  
(b) Current in 3Ω wire  
6
퐼2 =  
× 4퐴  
(i)  
P.d in the 1Ω wire  
6 + 3  
푉 = 퐼푅1  
1
퐼2 = 2.67퐴  
푉 = 4 × 1  
1
Example 04  
Two wires of 10Ω and 5Ω are in parallel,  
and the arrangement is in series with a 20Ω  
wire. If the current in the 5Ω wire is 2A,  
calculate the current in the 10Ω wire and the  
p.d V across the whole circuit.  
푉 = 4푉  
1
(ii)  
P.d in across the parallel wires,  
6Ω and 3Ω  
Solution  
푉 = 12푉 − 4푉  
2
Consider the diagram below which shows  
the conditions for the problem  
푉 = 8푉  
2
(iii)  
Current 푰ퟏ in the 6Ω wire.  
푣표푙푡푎푔푒  
푐푢푟푟푒푛푡 =  
푟푒푠푖푠푡푎푛푐푒  
8푉  
푐푢푟푟푒푛푡 =  
6Ω  
= 70V  
The total p.d on the parallel circuit = 70V  
Example 05  
Study the circuit below and answer the next  
questions  
Step 1: To find the P.d푽ퟏ in the 5Ω  
wire  
푉 = 퐼푅1  
1
푉 = 2 × 5  
1
푉 = 10푉  
1
Calculate the current when  
(i) The switch 퐾1 is closed while 퐾2 is  
open  
Step 2: To find the current in the 10Ω  
wire.  
(ii) Both switches 퐾1 and 퐾2 are closed  
(iii)Switch 퐾1is open and 퐾2is closed  
푉
1
푐푢푟푟푒푛푡 =  
푅
Solution  
10푉  
푐푢푟푟푒푛푡 =  
10Ω  
(i) When the switch 퐾1 is closed  
푐푢푟푟푒푛푡 = 1퐴  
Step 3: To find the current in the 20Ω  
wire.  
Current in the 20Ω wire = total current  
= 1A + 2A  
= 3A  
In this case the current will not flow in the  
wire with switch 퐾2  
Step 4: To find the P.d 푽ퟐ across the  
Step1: To find the resistance of the series  
20Ω wire  
circuit between 5Ω and the 3Ω resistors  
푉 = 퐼푅2  
2
Resistance in series = 푅1 + 푅2  
Resistance in series = 5Ω + 3Ω  
Resistance in series = 8Ω  
= 3 × 20  
= 60푉  
Step 5: To find the total P.d, V, across  
the parallel circuit  
Step 2: To find the total current in the  
circuit  
Total p.d = 10 + 60