Simple Circuit Analysis

In an examination you will be given a circuit diagram and expected to analyse it - calculate the voltage across a component or the current flowing thorugh it - or how much heat is dissipated in a given amount of time from a component.

In order to do this you need to understand how the potential difference supplied by the power supply gives energy to components depending upon their position in the circuit and their resistance.

Basic ideas and terms to grasp before you look at circuit diagrams:

Voltage (V ) is an electric potential difference. It is measured in volts (V) with a voltmeter connected in parallel across the points in the circuit you wish to compare. If there is a potential difference across two points in the circuit current will flow between them.

Charges ‘fall’ from high electric potential to low electric potential. A power supply therefore provides a ‘slope’ or potential gradient down which the charged objects (electrons or ions) will flow.

Current (I ) is the rate of flow of charge (Q ) through a component – how much charge moves in a given time. It is measured in amps (A) using an ammeter in series with the component you are interested in.

The charged objects that move in a wire are electrons. They are the electrons that are loosely held by the atoms that make up the wire.

The total amount of charge moving in a given time (current) depends on how many electrons move and how fast they move. The same current could be obtained by having double the number of charges moving at half the speed.

Resistance (R) is a measure of the reluctance of the conductor to allow the charges to move through it. It is measured in ohms (Ω). The resistance of a wire is affected by the material it is made from and its dimensions.

Conductivity of materials

Good conductors have loosely held outer shell electrons that they are 'happy' to allow to move away from the parent atom - they have low resistivity making their resistance lower than that of an insulator of the same dimensions.

Insulators hold on tightly to their electrons and do not let them wander therefore there are no free electrons to carry the charge and the resistivity of the material is high.

The structure of the atom the material is made of therefore has a big effect on the resistance of the material. This property is termed 'conductivity'.

Dimensions of the wire

A ‘wider’ wire (a wire of bigger diameter) has more electrons moving down the potential gradient provided by the power supply, therefore a wire of bigger diameter will allow a bigger current to flow through it if a given voltage is put across it. This makes its resistance smaller. The average drift velocity of the electrons does not change (the ‘slope’ is still the same steepness) – it is the increase in number moving that alters the current.

A longer wire has less volts per metre as the volts are shared out across more wire – the potential gradient is therefore not as steep and the average drift velocity of the electrons will be less making the current smaller. This means that a longer wire has a bigger resistance. The number moving in a given length of the wire is the same – it is the change in their drift velocity that changes the current.

When components are connected in series their resistances are added to give a sum total.

A useful fact - when components are connected in parallel the resistance of the whole parallel arrangement is always smaller than the resistance of the lowest value strand of the arrangement.

A useful shortcut - if you have N identical resistors of value R in parallel with each other the resistance of the whole arrangement is R/ N

Instruments you use

Ammeters have very low resistances. (They are made by connecting a low resistance shunt in parallel with a galvanometer to give them a very low resistance). They can therefore be connected in series with a component in a circuit without changing the resistance on that strand of the circuit by very much at all.

Voltmeters have a very high resistance, (They are made by connecting a high resistance shunt in series with a galvanometer to give them that very high resistance). They can therefore be connected in parallel with a component in a circuit without changing the resistance of the circuit by very much at all.

Once you are happy with these ideas you are ready to move on to the next stage.... Advice on the steps involved in analysing a circuit When it is okay to ignore the current through a voltmeter Why it is okay to take the voltage drop across an ammeter as zero Calculating the heat dissipated in a component

 

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