Physics Circuits

When you have resistors in series, to find the total resistance you only have to add the resistors together. For example if I had a resistor of 23 Ohms and a resistor of 32 Ohms in series, the Rtotal would be 23+32=55 Ohms. Therefore this is one of the more simpler parts of resistance. Furthermore, if you have 3 resistors in series, they will all add up together.

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Resistance in parallel is a little bit more tricky. In order to calculate it you must do 1over R1 + 1 over R2 + 1 over Rn with n being any of the resistors, up to how many resistors there are. This will always come up with a lower number and although that is quite a difficult concept to grasp, think of it as there are more paths for the energy to take so there will be less resistance in each path.

Electric current is the rate of flow of charge. It is the quantity of charge that passes through a surface (for example the cross section of a wire) per unit time. In electric circuits we usually think of the amount of charge that passes through a point on a wire per unit time.

The unit for electric current is the ampere, which is equal to as the number of coulombs of charge that pass a given point per second.

The average electric current can be calculated from:

I=ΔQΔt

where I  is the current, ΔQis the amount of charge flowing past the point and Δt is the amount of time taken for that amount of charge to pass that point.

Electric current through a component is measured using an ammeter, which is placed in series with the component. The resistance of an ideal ammeter is negligible, so that it has no effect on the rest of the circuit (when connected correctly in series with the circuit).

Electric current can be either alternatig (AC) or direct (DC). In alternating current, the direction of the current switches, whereas for direct current, the current always flows in the same direction but the magnitude may still vary.

Current in metal wires is usually transmitted by electrons, which each carry the same unit of charge, which is the negative of the elementary charge e=1.602×10−19Ce=1.602×10−19C. From this it can be seen that approximately 6×10186×1018electrons make up a coulomb of charge.

Current flow has a direction: the conventional current is defined as the direction of flow of positive charges. Since it is actually electrons that carry current in metal wired circuits, and electrons have negative charge, the motion of the electrons in the circuit is actually in the opposite direction to that of the conventional current.

It does not have to be electrons that carry current - any stream of charged objects may be considered as an electric current. In electrolytes there are both positive and negative ions. If a potential difference is applied, the positive ions will be attracted to the lower electric potential whereas the negative ions will be attracted to the higher electric potential. The positive and negative ions will be moving in opposite directions, and the current flow is the sum of the magnitudes of the two individual currents. For example, 1mAof positive ions flowing to the negative electrode in an ionic solution, and 1mAof negative ions flowing the other way, will show on an ammeter in the circuit as 2mA. Currents in electric currents are conserved at junctions due to conservation of charge. This process is described by Kirchhoff's first law.

I need to be able to find what quantity of charge moves past a point in the wire during a given period of time. This can be done by looking at what is happening inside the wire. We know that on average, the electrons move at their drift velocity ⟨v⟩. For the sake of visualisation, we can assume that all the individual electrons are actually moving at this velocity, because it makes no difference to the rate of flow of charge in the wire if we have many electrons and take the average flow rate. Therefore, in time Δt, all the electrons move a distance Δx, and hence the volume ΔV, which contains the electrons that pass surface S that runs perpendicular to the wire, is given by AΔx

The number of electrons contained within this volume is found by multiplying the volume, ΔV by n the number density of electrons, giving nAΔx. The charge contained within this volume, and thus the charge that passes surface S over time Δt, is found by multiplying this number of electrons by the elementary charge ee. This gives ΔQ=nAeΔx. Therefore we obtain:

I=nAeΔx over Δt

We know that ΔxΔt is simply the drift velocity of the electrons, so the final expression is:

I=nA⟨v⟩e