Introduction
Electrical circuits nearly always contain more than one component. For example, you can plug a radio, a toaster, and a microwave into different sockets in your kitchen but all will be connected to the same electricity supply.
Calculating the effective resistance of a combination of components allows circuit designers to prevent appliances from overheating or drawing too much current from the power supply.
For safety and other reasons, it is useful to know how the current in a circuit will vary depending on which appliances you use.
Electrical circuits nearly always contain more than one component. For example, you can plug a radio, a toaster, and a microwave into different sockets in your kitchen but all will be connected to the same electricity supply.
Calculating the effective resistance of a combination of components allows circuit designers to prevent appliances from overheating or drawing too much current from the power supply.
For safety and other reasons, it is useful to know how the current in a circuit will vary depending on which appliances you use.
Effective resistance
We sometimes call the network of wires and components connected to a power supply the external circuit or load circuit (since it is the powerconsuming part of the system). The total
resistance
The opposition to the flow of current provided by a circuit is called resistance. Resistance is measured in units called Ohms.resistance of the
external circuit
All the components connected across the terminals of a battery or power supply are collectively known as the external circuit.external circuit is sometimes called the load
resistance
The opposition to the flow of current provided by a circuit is called resistance. Resistance is measured in units called Ohms.resistance.Close the switches in Fig.1 to connect the batteries to the resistors. Set the variable resistor in circuit (b) to its maximum value by moving the slider as far up as it will go.
Click on the figure below to interact with the model.
The two circuits in the above diagram look very different indeed, but there are some similarities. Both circuits are powered from 9 V batteries and both contain a switch and an ammeter.
Now reduce the value of the variable resistor until the
current
The rate of flow of charge past any specific point in a circuit. The base unit of current is the Ampere.current in Fig.1(b) is equal to the current in Fig.1(a).When the current flowing from each of the 9 V batteries in Fig.1 is the same, we can say that both circuits have the same effective resistance.
Fig.1(a) looks complicated, but the 10 resistors connected to the 9 V battery are providing the same resistance as a single 75 Ω resistor! Fig.1(a) therefore has an effective resistance of 75 Ω. The effective resistance is also sometimes called the total resistance and is given the symbol R_{T}.
Resistors in series
Close the switch in each of the two circuits In Fig.2 below. We can see that the resistance in both circuits is the same
since equal currents flow from identical batteries. Therefore the effective resistance of both circuits in Fig.2 is the same.Click on the figure below to interact with the model.
From our earlier consideration of series circuits in the unit Current and Voltage, we can add labels to the circuit of Fig.2 as follows:
Click on the figure below to interact with the model.
Since the p.d.s across resistors in series add up we can say that: 
From Ohm's Law, 
So 
Therefore 
The effective resistance R_{T} of resistors R_{1} and R_{2} connected in series is determined by the equation:
Resistors in parallel
Fig.4 below shows a circuit in which a 100 Ω resistor is connected in series with a 9 V battery.Click on the figure below to interact with the model.
Connect the second 100 Ω resistor into the circuit and watch what happens to the current flowing from the battery.
At first it seems very strange that adding an extra resistor to create the
parallel circuit
Components connected in parallel offer alternative paths for charges from a supply.parallel circuit in Fig.4 makes it easier for current to flow. However the setup in Fig.5 might help clarify the situation.We can calculate the effective resistance of two resistors connected in parallel. In the circuits in Fig.6 below, the p.d.s across the resistors are all the same.
Click on the figure below to interact with the model.
The circuits in Fig.6 have the same resistance since the same total current flows from identical batteries. 
The total current into any junction I_{T} equals the total current flowing out of that junction, so

From Ohm's Law,

So

Simplifying this equation gives:

The effective resistance R_{T} of resistors R_{1} and R_{2} connected in parallel is determined by the equation:
This equation can be extended for any number of resistors in parallel.
For two resistors in parallel the equation can be rearranged into a more convenient form, giving the value of R_{T} if R_{1} and R_{2} are known: 
The effective resistance R_{T} of two resistors R_{1} and R_{2} in parallel can be determined from:
Resistors in practice
In circuit diagrams, resistors are represented as a rectangle and the value of the resistance is normally written as a number
beside the symbol.
In practice, resistors are normally very small and any text written on the resistor would be difficult to read. So the value of a resistor is usually indicated by a series of coloured bands around the body of the resistor. Each colour and each band has a value based on a standard colour code.
Summary
Connecting different components across a power supply alters the current flowing into an external circuit.
The effective resistance of components joined in series or parallel can be derived using the laws governing the behaviour of current and voltage in circuits.
Once the effective resistance of the components connected to a power supply has been determined the total current taken from the power supply can be calculated.
Connecting different components across a power supply alters the current flowing into an external circuit.
The effective resistance of components joined in series or parallel can be derived using the laws governing the behaviour of current and voltage in circuits.

Once the effective resistance of the components connected to a power supply has been determined the total current taken from the power supply can be calculated.
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