Where I is the current in Amperes, q is the charge in coulombs, and t is the time in seconds.

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Terence Brooks
5 years ago
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1 CURRENT ELECTRICITY What is current? All of use like to ask this little question, which is quite easily answered, but not so easily understood. Current is the flow of charges. In other words, the flow, or the flux (both mean the same, in case you are wondering) of electric charges is called electric current. Current is measured in terms of the rate of charge flow. In dimensional analysis, you might be interested to note, current is taken to be a basic quantity, with a unit Ampere. Since current is the rate of charge flow, so it is given as: Where I is the current in Amperes, q is the charge in coulombs, and t is the time in seconds. Unless you have noticed it, this means that 1 Ampere (A) is equal to 1 Coulomb (C) divided by 1 second (s). And this also means that: In other words, the charge is defined as: The quantity of unbalanced electricity in a body (either positive or negative) construed as an excess or deficiency of electrons. But this is not what we were looking for. Oh no. We were looking for the definition of a coulomb, and here it is: The coulomb is that charge passing a point in the circuit when there is a current of 1 Ampere that flows through that point of the circuit in a time interval of 1s. See the power of the equation! What we had to express in a whole statement could have been aptly described by the formula given above! So far we have discussed the basics of current electricity. Before moving on to the real topics of appeal, we will deal with just a few nifty pests. Conventional Current: it is always assumed that charges flow from positive to the negative terminal. This is not so. The actual flow is of electrons; and electrons move, simply putting it, from the negative terminal to the positive terminal in a circuit. Now, we know that Positive Terminal = High Potential Negative Terminal = Low Potential

2 There exists a potential difference through which the electrons travel. Now, if something moves from high to low potential, it is said to be moving along the potential gradient. But unless you have already noticed it, electrons move from low to high potential i.e. against the potential gradient. Now, this is against a well-accepted notion that things move from high to low potential. Therefore, just to satisfy our conventional legacy, we have assumed that a charge equivalent in value to the electrons flows from the positive to the negative terminal of the battery. This charge, which isn t actually existent, is termed the conventional charge. In current electricity, whenever we talk about current, we are talking about conventional current. In electronics we talk about electronic current but that is a separate matter. Potential Difference: We have already discussed this. However, it will be good for you to remember something you studied about work. Potential difference is related to the work done, or the energy transferred by the charge during its motion. This can be visualized by a simple mathematical formula: The unit of electric potential is Volt. From the above formula we can describe one Volt as the p.d. (potential difference) between two points, when 1 Joule of energy is transferred by one Coulomb of charge passing from one end to the other one. Electric Power: You might already know that power is the rate of doing work. Electrical power is just one more thing: it is the rate of transferring electrical energy. We know that: But W = qv, where q = It. So Or This is all mathematics, and mathematics is fun! A chappie named Einstein once said: Pure mathematics is, in its way, the poetry of logical ideas. You see, he had been right all along! We ll see some more ways of describing electric power in mathematical forms once we learn about Ohm s law and resistance. OHM S LAW Remember one simple thing: the existence of current is dependent on the existence of voltage. No voltage, no current (this changes rather dramatically in superconductors, but we haven t got there yet).

3 There was, in the Victorian era, a bloke named George Simon Ohm, who hailed from Prussia (modern day Germany). It was he who gave this law you are studying about a law which might be understood to be the focal point in electrodynamics. So what is the Ohm s law? The ohm s law is simply a statement which tells us that for any metallic conductor, the voltage applied, and the current are directly proportional. Yes, the more the voltage, the more the current. This is all very good, but one condition must be fulfilled: no change of physical state such as temperature must take place during the period of observation. In other words, the current must not be large enough to have a pronounced heating effect. In all proportionality relations, there is a factor known as a constant which relates the two quantities. This constant itself remains unchanged, and is indicative of the fact that the two quantities being related maintain a uniform relationship. In our case, this constant is resistance, denoted by R. Now Then The unit of R is, you will be surprised to know, named after this chappy it is ohm! Now let us review a few more equations: We know that electric power is equal to VI. Putting the value of V here: And if we put Here, we get Resistance: Till now, we have dealt with resistance only in mathematical terms. To understand it, consider what a real life resistance is. It is a hindrance; an obstruction that tries to stop motion. In the same way, an electric resistance is the obstruction that tends to stop the flow of electric charges. On what factors does resistance depends? Since it is a constant factor in Ohm s law, we may safely assume that it does not depend on either voltage or current. The resistance of a wire depends on: a. The nature of the wire. b. The dimensions (area and length) of the wire. c. The physical state of the wire or conductor. Resistance is directly proportional to the length, and it is inversely proportional to the area of cross section of the wire. This can be aptly understood by a simple analogy. A waiter has to cross a room full of little groups of people chattering and eating. If the room is longer and narrower,

4 he will find it relatively difficult to pass, and will encounter more resistance. If the room is wider, he will experience less resistance, and will pass through easily. In mathematical terms: Where is the resistivity of the conductor. Now resistivity is a new term. It is defined as a measure of the resisting power of a specified material to the flow of an electric current. In other words, resistivity is material specific: if we have a wire of constantan (a Cu-Ni alloy), its resistivity will not change if we change its area or length. However its resistance will change if we do so. Resistivity is mathematically defined as: The units of resistivity are Ωm (ohm meter). Types of Materials: Devices which conduct electricity may be differentiated into those that follow ohm s law (ohmic) and those that do not do so (non-ohmic). For a device to be ohmic, the current passing through it should be directly proportional to the voltage applied. This type of device gives a straight line in a current-voltage graph, as shown below. A constantan wire is ohmic. We see, that for a filament lamp which uses a tungsten wire, the straight line proportionality is lost after some time. This is due to the heating effect of current due to which the temperature of the filament may rise up to 1500 C, which is described later. Thus a tungsten wire is nonohmic. We see that the diode is also non-ohmic. This is because of the fact that the semiconductor diode has a negative temperature coefficient of resistance α. We will discuss it more thoroughly below.

5 Resistance and Temperature: We have up till now, talked about resistance alone. What, one wonders, is the reality of electrical resistance? When charges move across a conductor, they find atoms blocking their way. The charges may collide with these atoms and lose some of their energy as heat. Thus the charges experience a hindrance to their free movement or flow. What happens when we increase temperature? We know that temperature is directly proportional to kinetic energy. In the case of solids, the atoms possess vibrational K.E. If the temperature is increased, this vibrational K.E. increases. Now there is a greater chance that an atom may collide with a free electron and obstruct its way. Thus the collision frequency has increased. This means that the resistance increases with temperature. Now, what is this temperature coefficient of resistance? It is simply a fractional change of resistance per degree kelvin rise of temperature. Don t get it? You will soon enough. Consider a wire whose resistance is being taken at zero degrees, and at t degrees of temperature. These are expressed respectively as R o and R t.. The change in resistance is given as: Now, this change depends directly on both the temperature t and the original resistance R o. This is represented as: Where α is the temperature coefficient of resistance. It is given as: Thus the temperature coefficient of resistance is defined as the fractional change in resistance per temperature rise in Kelvin. The unit, as you can well guess, is per Kelvin or K -1. When we say that substances have a positive temperature coefficient of resistance, we mean that with the rise of temperature, their resistance increases. But when we say that they have a negative temperature coefficient of resistance, it means that their resistance decreases with temperature increase. This fact applies to semiconductor diodes, whose resistance drops as the temperature rises. Now, I believe we have covered enough about resistance and resistivity to satisfy all your needs. Don t worry, there is something coming up that will test your intellectual powers to the extreme. Stay tuned! COMBINATION OF RESISTORS All of you might have noticed that in some cases, when we want to block someone s way, we place a series of hurdles to stop them. This same thing can take place with resistors too. A resistor represents a definite value of resistance. If I have a resistor of 10Ω, it means that when connected in a circuit, it will set up a resistance of 10Ω to the charge flow.

Resistors can be connected in two ways: in series and in parallel. In these cases, we deal with the equivalent resistance of these combinations. What, you might ask, is the equivalent resistance?

6 Resistors can be connected in two ways: in series and in parallel. In these cases, we deal with the equivalent resistance of these combinations. What, you might ask, is the equivalent resistance? It is the sum of all the resistances put together in a single resistance. Suppose I have 5 blocks each weighing 10 grams. If I replace them with a single block of 50 grams, the overall effect will be the same. That is what equivalent resistance is about. We ll deal with the two combinations separately: 1. Series Combination: In this case, all the resistances are connected in series. Their equivalent resistance is simply calculated by adding them up. Consider the figure: Here, the equivalent resistance can be simply calculated as the sum of R1, R2 and R3 i.e. 150Ω. So, for any series connection: Also remember that in a series connection, the current is not divided, as it has no alternate route to follow. However, the potential difference is divided across each of the resistances. Also, remember that in a series connection, the equivalent resistance has a value greater than any individual resistance in the circuit. 2. Parallel Combination: Here, the sum of reciprocals of individual resistances constitutes the reciprocal of the equivalent resistance. It is a roundabout way of putting it, but well. See this figure, now: In this case, the current, coming from one side, is offered three paths to reach the other side. Remember that current always flows through that circuit which has the least resistance. The P.D. in this case will be the same across each of the resistors. The equivalent resistance in this case is given as:

Thus the equivalent resistance in this case is less than the least component of the circuit. Note: There is mathematics involved in deriving all these formulas.

7 Thus the equivalent resistance in this case is less than the least component of the circuit. Note: There is mathematics involved in deriving all these formulas. For a simple exam level, you won t be really needing that. So, I ve skipped it a bit. Up till now, we have studied some very simple combinations. Now, we will deal with the complex combinations. I ll not solve them in full: just a few hints, and you will do fine! Some Complex Circuits: 1. The Triangle Circuit Hint: 2 in series, one parallel. 2. A simple one in a complex mood Hint: Try weaving your path straight down. Look for left and right. It s really simple. 3. The best brainteaser I ve seen in years:

zero, so if the current, and that resistor does not

8 Hint: Nah, don t spiral it. It s simpler than you think. Just remember that where the potential difference is zero, so if the current, and that resistor does not count. 4. Another trickster Hint: When everything goes parallel..

PHYSICS FORM 5 ELECTRICAL QUANTITES

PHYSICS FORM 5 ELECTRICAL QUANTITES QUANTITY SYMBOL UNIT SYMBOL Current I Amperes A Voltage (P.D.) V Volts V Resistance R Ohm Ω Charge (electric) Q Coulomb C Power P Watt W Energy E Joule J Time T seconds s Quantity of a Charge, Q Q = It