A circuit is a closed loop that electrons can travel in.

Components of a circuit:

Cell or a Battery (many cells)
This provides a voltage to get the current flowing in a circuit. 

Voltmeter: 
It is an instrument used for measuring potential difference between two points in an electric circuit. 

Ammeter: 
It is an instrument used for measuring current in an electric circuit. 
Resistor: 
Resistors are used to reduce current flow. 

Lamp:
A lamp is used to determine whether or not electricity is flowing. 

Switch:
A switch is used to turn the flow of electiricy on or off. 
In an open switch, the wire is not connected. Therefore, no electricity flows if the switch is open. 
In a closed switch, the wire is connected. Therefore, electricity flows if the switch is closed. 

Components of a circuit
Components of circuit

Series Connections

If components are connected one after the other in the same loop, then the circuit is in series. 

resistors are in series

In the above circuit, the resistors are place one after the other. Therefore, they are said to be in series. 

Voltage in Series Circuits
The potential difference (voltage) across both resistors must add up to give the potential difference of the battery. 

Let us say voltage across first resistor (R₁) = A
Let us say voltage across second resistor (R₂) = B
Therefore, voltage across battery = A + B

Let us say voltage across first resistor (R₁) = 4 V
Let us say voltage across second resistor (R₂) = 8 V
Therefore, voltage across battery = 4 + 8 = 12 V

Current in Series Circuits
The current across both resistors will be the same. 
Current R₁ = Current R₂ = Current across battery

Let us say current across first resistor (R₁) = 4 A
Then, current across second resistor (R₂) = 4 A
Therefore, resistance of circuit = 4 A

Resistance in Series Circuits
To calculate the total resistance of the circuit, we add the resistance of each of the resistors. 

Let us say resistance of first resistor (R₁) = A
Let us say resistance of second resistor (R₂) = B
Therefore, resistance of circuit = A + B

Let us say resistance of first resistor (R₁) = 4 Ω
Let us say resistance of second resistor (R₂) = 8 Ω
Therefore, resistance of circuit = 4 + 8 = 12 Ω


Parallel Connections

In a parallel circuit, the current divides into two or more paths before recombining to complete a circuit. 

resistors are in parallel

In the above circuit, there are two branches, each with one resistor. 

Voltage in Parallel Circuits
The potential difference (voltage) across both resistors is equal. The potential difference across the battery is equal to the potential differences across each of the resistors. 

Let us say voltage across first resistor (R₁) = A
Then, voltage across second resistor (R₂) = A
Therefore, voltage across battery = A 
Voltage across R₁ = Voltage across R₂ = Voltage across battery

Let us say voltage across first resistor (R₁) = 4 V
Then, voltage across second resistor (R₂) = 4 V
Therefore, voltage across battery = 4 V

Current in Parallel Circuits
However, the sum of the currents across R₁ and R₂ is equal to the current across the battery. 

Let us say current across first resistor (R₁) = A
Let us say current across second resistor (R₂) = B
Therefore, current across battery = A + B
Current across R₁ + Current across R₂ = Current across battery

Let us say current across first resistor (R₁) = 4 A
Let us say current across second resistor (R₂) = 8 A
Therefore, current across battery = 8 + 4 = 12 A

Resistance in Parallel Circuits
Let total resistance = Rₓ
To calculate the resistance of the circuit, we use a formula: 

¹⁄Rₓ = ¹⁄R₁ + ¹⁄R₂

Let resistance of R₁ = 4 Ω
Let resistance of R₂ = 8 Ω
¹⁄Rₓ = ¹⁄₄ + ¹⁄₈ = ³⁄₈
Rₓ = ⁸⁄₃
Rₓ = 2.666 ≈ 2.67 Ω