CURRENT ELECTRICITY

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Electrical Quantities

Notes from Erica, 1 September 2020

As we all have learned in Physics class, electric current is produced when electrons move. Movement of electrons is that when a charged object (it is charged by the electrons that are added to or removed from it) is provided with a conducting path, electrons start to flow through the path from or to the object. Hence, a current is a flow of charge. Since an electric current is the rate of flow of electric charge, which is calculated by dividing charge by the time taken (I = Q/t ; I = current (in A), Q = charge (in C) & t = time taken in second) to determine the amount of electric charge that passes through a conductor per unit time, thus it is measured in amperes. 1 ampere is the electric current produced when 1 coulomb of charge passes a point in a conductor in 1 second. & to measure the strength of an electric current in an electric circuit we should use an ammeter.

The formula that I’ve written above, can be altered to find the charge, and it would be charge = current x time. An example for this formula, we will be taking the current as 0.2 A and the time is 2 hours. And to find the total electric charge, first off we need to convert the time from hours to seconds; 2 hours is equal to 7200 seconds when converted. And now the calculation of the electric charge will be 0.2 A x 7200 seconds, which will give us 1440 C = 1.4 x 10³ C as the final answer.

Moving on to the electromotive force of an electrical energy source, it is the work done by the source in driving a unit charge around a complete circuit. The electromotive force is not actually a force and its unit is not newton as all forces do, but it is volt (V). Electromotive force is calculated by dividing the work done (in J) (for example the amount of non-electrical energy converted to electrical energy) by the amount of charge (in C), hence we know that e.m.f of an electrical energy source is 1 volt if 1 joule of work is done by the source to drive 1 coulomb of charge completely around circuit. In conclusion its formula is ε = W/Q, and thus to find volt, we just need to divide the work done in Joules by the amount of charge in coulomb.

Now to the cell arrangement which can be in series or parallel that affects the e.m.f. ; not only the arrangement but also the number of dry cells will also determine the amount of e.m.f. supplied to an appliance.

Examples & explanations of calculation of the total e.m.f of a circuit:

1. 2 dry cells, each has 1.5 J/C, are connected in series in a circuit. Determine the electromotive force as a result of this arrangement of dry cells?

To find the answer to this question, first since it is a series circuit, the resultant e.m.f. will be larger than the e.m.f. of each cell which is 1.5 J/C, because the charges will gain energy as they pass through each cell. To find the resultant e.m.f we should add both e.m.f, 1.5 V + 1.5 V = 3.0 V, so the answer to the question is 3.0 V. Thus the cells will last for a shorter time compared to a parallel circuit.

2. 2 dry cells, each has 1.5 J/C, are connected parallel to each other. What is the electromotive force of this combination?

And now it is a parallel circuit, which is when the resultant e.m.f. is equal to that of a single cell, since the charge gains only a portion of the energy from each cell. So the answer to this question is 1.5 V. And thus the cells will last for a longer time compared to those in a series circuit.

Examples of different types of cell arrangement used in daily life:

• Series arrangements are usually used in the refrigerator and freezer, which are in the compressor and the temperature control switch. If the temperature inside the refrigerator/freezer gets too hot, the temperature control switch will turn the compressor on until the temperature drops.

• Parallel arrangements are used throughout your home for electricity because they allow current to keep flowing through various paths thus there won’t be a problem that the current is unable to flow through a path. Usually parallel arrangement is also used in remote controllers.

Note that it is not advisable to combine 2 energy sources e.g. dry cells parallel with each other when they have different electromotive force. Since in a series circuit they can just be added together, but in the parallel circuit case, the larger e.m.f. will charge the other e.m.f., but the circuit components will be very hot because the energy has been transformed into heat, leading to waste of energy and in conclusion it is dangerous since it may explode. Thus there should be an equal voltage source of e.m.f. arranged in parallel to make a battery safely.

Next is potential difference, as what we know the potential difference (p.d.) across a component in an electric circuit is the work done to drive a unit charge through the component. It is measured in volts and to find it, we have the formula V = W/Q, where V is the potential difference or voltage across a component (in V), W is the work done, (e.g, amount of electrical energy converted to other forms) (in J) and Q is the amount of charge (in C). Thus from this formula we can know that, for each coulomb of charge passing through the component, the amount of electrical energy converted to other forms of energy is called the potential difference.

(Note that e.m.f. and p.d. have the same unit and measured with the same instrument which is voltmeter, but e.m.f. is provided by a source of electrical energy, but p.d. refers to the electrical energy converted to other forms by a circuit component. And also the emf transmits current throughout the circuit, while pd transmits current between any 2 points.)

And last is a short brief of resistance, the resistance of a component is the ratio of the potential difference across it to the current flowing through it. The resistance of a component is a measure of the opposition an electric current experiences when it flows through the component. Its formula is R = V/I ; where R stands for the resistance of the component (in Ω), V is the potential difference across the component (in V) and I is the current flowing through the component (in A). By that we know that by a given potential difference, the higher the resistance, the smaller the current passing through it. And it is affected by length, area, resistivity and also temperature.