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Background

In our day today life, we interact with electrical devices such as bulbs, torches, iron boxes, refrigerators, radios, television sets among others.This topic will have the following sub-topics: Introduction, Ohm's law, Resistance, Resistors, Arrangement of resistors, Determination of effective resistance and Application of current electricity.

Objectives

By the end of the topic, you should be able to:

- Define an electric current

- Set up a simple circuit

- Determine the relationship between current (I) through a conductor and voltage(V) across it at fixed temperature

- Define resistance

- Distinguish between series and parallel arrangement of resistors in a circuit.

- Determine the effective resistance of resistors arranged in series and parallel

- State and explain some applications of current electricity










Introduction

In Form 1, we discussed about an electric current, a bulb, a dry cell, a switch, circuit symbols and simple circuits. We learnt circuit symbols like for a bulb, a switch, a voltmeter, an ammeter a fixed resistor, a variable resistor and others. Construct a simple circuit which has a bulb, connecting leads, voltmeter, ammeter, switch and cells by dragging and dropping. See the circuit components which are supposed to be dragged and dropped in their right positions.

Ohm's law

When potential difference is created across a conductor current will flow. It is therefore important to determine how the two variables relate. To understand this relationship do the following:



Observations

The graph obtained is a straight line graph passing through the origin.



Discussion

A graph of voltage against current is a straight line passing through the origin. This shows that voltage is directly proportional to current (V A I) hence V = IR. The gradient of such a graph gives resistance, R.

Conclusion

The relationship between voltage and current is known as Ohm's law and it states that current flowing through a conductor is directly proportional to the voltage across it provided temperature and other physical factors remain constant. The relationship (Ohm's Law) can be expressed as V A I which is further expressed as V = constant x I. The value of the constant is the resistance, R of the material.

Resistance

The collision between electrons and atoms hindering the movement of the electron is called resistance. Resistance is the opposition to the flow of an electric current and its SI unit is the Ohm (Q). Play the animation below to see how this happens.

Series arrangement of resistors

The illustration below shows a series connection of resistors. Click on the word series to observe a series arrangement of resistors

Parallel arrangement of resistors

The illustration below shows a parallel connection of resistors. Click on the word parallel to observe a parallel arrangement of resistors.

Derivation of formulae for effective resistance.

Series arrangement

Before we start deriving the formula for effective resistance for this case, it is worth noting that current is constant throughout the circuit. From V = V1+ V2 but V1 =IR1 and V2= IR2 Hence IRT = IR1 +IR2. IRT = I (R1 + R2). RT = R1 + R2. The total or effective resistance for the two resistors in series is given by:

RT= R1 + R2.

If the resistors are three,RT= R1 + R2 + R3

If we have n resistors, then RT = R1 + R2 + R3 +.......+ Rn.


Parallel arrangement

In parallel arrangement, the voltage across each resistor is the same. From Ohm's Law V = IR, therefore I = V/R, when current I is made the subject of the formulae.
Hence VT/RT = VT/R1 + VT/R2.
VT/RT = VT (1/R1 + 1/R2) VT can be factored outside the brackets and then the equation is divided by VTon both sides hence simplified as;
1/RT = 1/R1 + 1/R2
If the resistors are three,
1 /RT = 1/R1 + 1/R2 + 1/R3.
If we have n resistors, then 1/RT = 1/R1 + 1/R2 +..........+ 1/Rn

In general, the total resistance for resistors in series is the sum of all the resistors.

Application of resistors

There are several day-to-day application of resistors and resistance. As we learnt previously resistors are used regulate the amount of current, different electronic and electrical gadgets require different types and sizes of resistors. The following are some of the common applications.

Fuse

The fuse is used in most household electrical gadgets such as electric iron boxes, sockets among others to regulate the amount of maximum current permissible in the respective gadget. To understand how the fuse protects these devices close the switch and vary current such that it rises beyond 5A as you observe the bulb. What happens? Click the play buttons provided and make your observations.

Observation

The fuse blows when the current exceeds 5A.

Explanation

When current passes through a thin resistor as the fuse the temperature rises and melts the wire hence disconnecting the circuit and no current flows. Therefore fuses are a thin wire with low melting point which breaks the circuit to protect devices from high currents which could be destructive to the device.

Arrangement of bulbs and fluorescent tubes

Another common application of resistance is in the arrangement of lights in houses, offices and other places. Bulbs and fluorescent tubes are normally arranged in parallel so as to ensure equal voltage and maximum lighting across them.

Potentiometer

A Potentiometer is commonly used in most household devices such as radios, television sets among others. This is a device that regulates resistance hence the amount of current flowing in a radio can be regulated using it.


Arrangement of resistors

Arrangement of resistors The way resistors are arranged will affect the amount of current flowing in a given circuit and the voltage across any two points. In case of a bulb, it can affect its brightness. Resistors are either connected in series or in parallel. Click on the play button to observe these two possible arrangements.

Observations

We have observed that for three resistors in parallel connection the brightness of the bulbs is more than in a single resistor and brightest for three resistors in parallel. The bulb is bright for resistors in series, brighter for a single resistor and brightest for resistors in parallel.

Conclusion

The brightness of the bulb indicates the total amount of current flowing in the circuit and which is determined by the total resistance (effective resistance) of the circuit. When resistors are arranged in series the total resistance increases and hence current decreases; whereas when the same resistors are arranged in parallel the total resistance reduces and hence current increases.

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