This document describes electric circuits and the differences between series and parallel circuits. It includes: - Descriptions of circuit components like cells, batteries, resistors, and switches used to draw circuit diagrams. - Explanations of how current, voltage, and resistance work in series circuits compared to parallel circuits. In series circuits, the same current flows through each component and voltage drops add up. In parallel circuits, currents split and voltages are equal across each branch. - Examples of calculating current, voltage, resistance, power, and solving circuit problems for both series and parallel circuits using formulas like Ohm's law.

1. UNIT 2
Electric Circuits
AGORA International School
Technology
3 ESO

2. 1. ELECTRIC CIRCUITS:
Closed loop of electrical components around which current can
flow, driven by a potential difference
SECTION 1
Series and Parallel
Circuits
1. Electric Circuits
1.1. Circuit Diagrams
1.1. How To Draw Circuit Diagrams
Circuit symbols are used in circuit diagrams showing how a circuit is connected
together.
Wire
Connects components and passes current easily
from one part of a circuit to another.
Cell
Supplies electrical energy. The larger line is
positive (+).
Battery
Supplies electrical energy. A battery is more than
one cell.
Switch
Current flows only when the switch is in the
closed (on position).
Resistor
A resistor restricts the flow of charge (for example
to limit the current passing through an LED)
Lamp
A transducer which converts electrical energy to
light.
SERIES AND PARALLEL CIRCUITS

3. Use circuit symbols to construct schematic diagrams for the following circuits:
SERIES AND PARALLEL CIRCUITS
a. Two cells, one light, and one
switch
b. A single cell, a resistor, a lamp
and a switch
c. Three cells are placed in a
battery pack to power a circuit
containing three light bulbs.
SECTION 1
Series and Parallel
Circuits
1. Electric Circuits
1.1. Circuit Diagrams

4. 2. TYPES OF CIRCUITS:
There are two types of electrical circuit, parallel circuits and series circuits.
2.1 Series Circuits
Each lamp is connected in a manner such that there is
only one pathway by which charge can pass. Each charge
passing through the loop will pass through each resistor
in consecutive fashion.
SERIES AND PARALLEL CIRCUITS
Current Voltage Resistance
The current that goes
through the first light
bulb must go through
the second and third
light bulb. The same
current flows through
each bulb, even if the
bulbs are not identical.
The battery provides a
certain amount of
energy to every
coulomb of charge.
The energy in the
circuit is distributed to
the resistors (lamps) in
the circuit.
The total resistance of
the circuit is found by
simply adding up the
resistance values of
the individual resistors.
IT = I1 = I2 = I3 VT = V1 + V2 + V3 RT = R1 + R2 + R3
SECTION 1
Series and Parallel
Circuits
1. Electric Circuits
1.1. Circuit Diagrams
2. Types of Circuits
2.1. Series

5. SERIES AND PARALLEL CIRCUITS
SERIES CIRCUIT SUMMARY
SERIES PARALLEL
Current
All components have the
same (equal) current.
IT = I1 = I2 = I3
Voltage
Drops add to equal total
voltage.
VT = V1 + V2 + V3
Resistance
Add to equal total
resistance. The more
resistors in the circuit, the
larger the total resistance.
RT = R1 + R2 + R3
Ohm’s
Law
Ohm’s law can be applied
to the entire circuit or to
any resistor in the circuit.
VT = IT ∙RT
V1 = I1 ∙R1
V2 = I2 ∙R2
Power
Power can also be
calculated for the entire
circuit or for any resistor
in the circuit.
PT = VT ∙ IT
P1 = V1 ∙I1
P2 = V2 ∙I2

6. SERIES AND PARALLEL CIRCUITS
Sample Problem 1
Given the following series circuit, find:
a) the total resistance
b) the total current
c) the current through each resistor
d) the voltage across each resistor
e) the total power
f) the power dissipated by each resistor
STEP 1: Identify Data
VT = 24V
R1 = 3 Ω
R2 = 5 Ω
R3 = 4 Ω
R1 = 3 Ω
R2 = 5 Ω
R3 = 4 Ω

7. SERIES AND PARALLEL CIRCUITS
Sample Problem 1
Given the following series circuit, find:
a) the total resistance
b) the total current
c) the current through each resistor
d) the voltage across each resistor
e) the total power
f) the power dissipated by each resistor
Strategy: This is a series circuit. All the current
goes through each of the resistors. First
calculate the total resistance. Then, using Ohm’s
law, calculate the total current. You can also use
Ohm’s law to calculate the voltage across each
resistor. Then, using the equation for power,
calculate the total power and the power
through each resistor.
R1 = 3 Ω
R2 = 5 Ω
R3 = 4 Ω
STEP 2: Plan a Solution
1) Find total resistance: RT = R1 + R2 + R3
2) Find total current: 𝐼 𝑇 =
𝑉 𝑇
𝑅 𝑇
,
3) Find all the voltages 1, 2 and 3: V1 = I1 ∙R1 ; V2 = I2 ∙R2;
V3 = I3 ∙R3 (Check the sum of the voltage drops is equal
to the voltage supplied by the battery.)
4) Find all the powers T, 1, 2 and 3: P1 = V1 ∙I1 ; P2 = V2 ∙I2;
P3 = I3 ∙V3 (Check the sum of the powers in the resistors
is equal to the power supplied by the battery.)
*And since it is a series circuit, the total current will be
equal to the currents in all the resistors IT = I1 = I2 = I3

8. SERIES AND PARALLEL CIRCUITS
Sample Problem 1
Given the following series circuit, find:
a) the total resistance
b) the total current
c) the current through each resistor
d) the voltage across each resistor
e) the total power
f) the power dissipated by each resistor
R1 = 3 Ω
I1 = 2 A
V1 = 6 V
P1 = 12 W
R2 = 5 Ω
I2 = 2 A
V2 = 10 V
P2 = 20 W
VT = 24 V
IT = 2 A
RT = 12 Ω
PT = 48W
R3 = 4 Ω
V3 = 8 V
I3 = 2 A
P3 = 16W
Solution:
VT = V1 + V2 + V3
24 V = 6 V +10 V + 8 V
PT = P1 + P2 + P3
48 W = 12 W + 20 W + 16 W
Check:

9. 2.2 Parallel Circuits
Parallel circuits have multiple pathways by which charge
can pass. When arriving at the branching location (node),
a charge makes a choice as to which branch to travel
through on its journey back to the low potential terminal.
SERIES AND PARALLEL CIRCUITS
Current Voltage Resistance
The current splits at
certain junctions and
then joins together at
other junctions. The
current entering any
junction must equal the
current leaving that
junction if charge is to
be conserved.
In a parallel circuit, the
charges that go
through one resistor do
not go through any
other resistor. All of the
energy of that charge
must be transferred to
that one resistor.
The total resistance of a
set of resistors in
parallel is found by
adding up the
reciprocals of the
resistance values, and
then taking the
reciprocal of the total
IT = I1 + I2 + I3 VT = V1 = V2 = V3
1
𝑅 𝑇
=
1
𝑅1
+
1
𝑅2
+
1
𝑅3
SECTION 1
Series and Parallel
Circuits
1. Electric Circuits
1.1. Circuit Diagrams
2. Types of Circuits
2.1. Series
2.2 Parallel

10. SERIES AND PARALLEL CIRCUITS
SERIES CIRCUIT SUMMARY
SERIES PARALLEL
Current
All components have the
same (equal) current. IT = I1 = I2 = I3
Currents through each
component add to equal
total current.
IT = I1 + I2 + I3
Voltage
Drops add to equal total
voltage.
VT = V1 + V2 + V3
All components have the
same (equal) voltage.
VT = V1 = V2 = V3
Resistance
Add to equal total
resistance. The more
resistors in the circuit, the
larger the total resistance.
RT = R1 + R2 + R3
The more resistors in the
circuit, the smaller the
total resistance of the
circuit.
1
𝑅 𝑇
=
1
𝑅1
+
1
𝑅2
+
1
𝑅3
Ohm’s
Law
Ohm’s law can be applied
to the entire circuit or to
any resistor in the circuit.
VT = IT ∙RT
V1 = I1 ∙R1
V2 = I2 ∙R2
Ohm’s law can be applied
to the entire circuit or to
any resistor in the circuit.
VT = IT ∙RT
V1 = I1 ∙R1
V2 = I2 ∙R2
Power
Power can also be
calculated for the entire
circuit or for any resistor
in the circuit.
PT = VT ∙ IT
P1 = V1 ∙I1
P2 = V2 ∙I2
Power can also be
calculated for the entire
circuit or for any resistor
in the circuit.
PT = VT ∙ IT
P1 = V1 ∙I1
P2 = V2 ∙I2

11. SERIES AND PARALLEL CIRCUITS
Sample Problem 2
Given the following series circuit, find:
a) the current through each resistor
b) the total current
c) the total power
d) the power in each resistor
e) the total resistance
Strategy: This is a parallel circuit. The current follows different paths to each resistor. In a parallel circuit,
the voltage drops across each resistor are equal. In this case, the voltage of each resistor equals 24 V.
VT = V1 = V2 = V3
You can put this information in the diagram immediately. Once you know two of the four variables (V, I, P,
R), you can find the other two variables. In this case, you know V and R. You can find the current using
Ohm’s law for each resistor.
R3 = 4 ΩVT = 24 V
STEP 1: Identify Data
VT = 24V
R1 = 8 Ω
R2 = 6 Ω
R3 = 12 Ω
R1 = 8 Ω R2 = 6 Ω R3 = 12 Ω

12. SERIES AND PARALLEL CIRCUITS
Sample Problem 2
Given the following series circuit, find:
a) the current through each resistor
b) the total current
c) the total power
d) the power in each resistor
e) the total resistance
STEP 2: Plan a Solution
1) Since it is a parallel circuit, the total voltage will be equal
to the voltages in all the resistors VT = V1 = V2 = V3
2) Find the currents 1, 2, 3 : 𝐼1 =
𝑉1
𝑅1
; 𝐼2 =
𝑉2
𝑅2
; 𝐼3 =
𝑉3
𝑅3
3) You can find the total current by adding the currents
through each resistor. If the resistors have current IT = I1
+ I2 + I3
4) Use the power equation to calculate the power once
you know the current. T, 1, 2 and 3: PT = VT ∙IT; P1 = V1
∙I1 ; P2 = V2 ∙I2; P3 = I3 ∙V3
5) You can find the total resistance of the circuit easily by
using Ohm’s law for the entire circuit : 𝑅 𝑇 =
𝑉 𝑇
𝐼 𝑇
R3 = 4 Ω
R3 = 12 ΩR2 = 6 ΩR1 = 8 Ω
VT = 24 V
5’) You can also find the total resistance by adding the
individual resistors in parallel. Notice that in this
equation, you are dealing with fractions.
1
𝑅 𝑇
=
1
𝑅1
+
1
𝑅2
+
1
𝑅3

13. SERIES AND PARALLEL CIRCUITS
Sample Problem 2
Given the following series circuit, find:
a) the current through each resistor
b) the total current
c) the total power
d) the power in each resistor
e) the total resistance
R1 = 8 Ω
V1 = 24 V
I1 = 3 A
P1 = 72 W
VT = 24 V
IT = 9 A
RT = 2,67 Ω
PT = 216 W
R2 = 6 Ω
I2 = 4 A
V2 = 24 V
P2 = 96 W
R3 = 12 Ω
I1 = 2 A
V3 = 24 V
P3 = 48 W