Specific objectives.

• Define p.d and e.m.f and state their SI units.
• Explain internal resistance.
• Measure p.d and electric current in a circuit.
• Verify Ohmâ€™s law.
• Find resistance and state its SI unit.
• Determine experimentally the voltage current for various conductors.
• Write the formula for effective resistance of resistors in series and in parallel.
• Solve numerical problems involving Ohmâ€™s law. Resistance in series and in parallel.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Electric current.

• Electricity â€“ is the effect of electric charges.
• Static electricity â€“ is electricity produced by static charges.
• Electrostatic â€“ is the study of effect of electric charges.
• Dynamic electricity â€“ Is electricity produced by moving or flowing charges. This is the main electricity which produces electric current hence electric energy.
• There are two types of currents namely;
1. Alternating current (a.c)
2. Direct current (d.c)

Electric current.

• Is the rate of flow of electric charges.
• The quantity of charges Q is measured in Columbs (C).

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Q = It

• Is measured in amperes using an ammeter

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  1 Q = 6.25 x 1018

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Electric circuit.

• Is the path followed by electric current or electric charges.
• Consists of the source of charges â€“ cell or generator, conductors, meter (ammeter and voltmeter) and appliances such as bulbs.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Cell.

• An electric device that store electric energy in form of chemical energy and drives electric current around a circuit.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Types of cell.

1. Open circuit.
• This is a circuit where charges do not flow.
1. Closed/complete circuit.
• This is a circuit where charges flow.
• The electrons travel from the negative terminal of the cell to the positive terminal.
• Electric current flows from the positive terminal of the cell round the circuit of the negative terminal. This is called conventional current.
1. Short circuit.
• Is a circuit where a conductor is used to make current bypass an appliance.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Flow of electric current.

• The charges do not flow in a conductor unless they are forced to do so by the cell.
• They have to be given some energy. For this reason, a cell or a source has to set up energy difference across the ends of the conductor.
• The flow of electric current along a conductor is similar to the flow of water along a pipe. Water will flow from one end of the pipe to the other end when the two ends have a difference in height, level or potential energy.
• In a similar way, electric charges will flow along a conductor when the two ends have electrical energy difference called electrical potential energy difference (p.d).

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Potential difference.

• Is the energy per columb released by a cell when electric current flows from one point of a conductor to the other.

Â Â Â Â Â Â Â Â Â Â Â  p.d =Â  E/Q =E/ItÂ  Â  Â  but E/tÂ  = power

Â Â Â Â Â Â Â Â Â Â Â  p.d =power/amperesÂ  =w/a

• d is power per amperes produced by a cell or generator when electric current flows through a conductor.

Â Â Â Â Â Â Â Â Â Â Â  V = Power = VI

• The direction of the current is always from a high p.d to a lower p.d. A large p.d gives a large current.
• A voltmeter is always connected across two points to measure the difference in potential between two points.
• The amount of p.d a cell can provide depends on two factors.
1. Electromagnetic force (e.m.f)
2. Internal resistance of a cell.

Electromagnetic force (e.m.f).

• This is the total energy per columb produced by a cell or battery.
• It is the total power per amperes a cell or battery can provide.
• It is equal to the p.d across the cellâ€™s terminal when the cell is not connected to an external circuit.
• It is measured in volts.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Internal resistance.

• Is the ability of a cell to resist or oppose the flow of electric current through it.
• It is measured in Ohms (É² )by an ohmmeter.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Resistors.

• Are conductors that offer an opposition to the flow of electric current.
• This opposition is called resistance and it is measured in Ohms by an ammeter.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Factors affecting resistance.

1. Length .
• A conductorâ€™s ability to resist the flow of current is directly proportional to the length.
• A longer conductor has a high resistance.
1. Cross- section area.
• The resistance of a conductor is inversely proportional to the cross- section area of a conductor.
• A thin wire has high resistance than a thick wire.
1. Material.
• Good conductors e.g. silver, copper and aluminium have low resistance or no resistance than bad conductors.
1. Temperature.
• The conductorâ€™s resistance is directly proportional to temperature.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Resistivity.

• Is the resistance of unit length of a conductor of unit cross- section area at constant temperature and pressure.

Â Â Â Â Â Â Â Â Â Â Â  R

Â Â Â Â Â Â Â Â Â  R = Pl/A

Â Â Â Â Â Â Â Â Â  P =RA/LÂ  Â  Â  =Â Â Â Â  where P is a constantÂ Â  SI unit = É²m

Â

Â Â Â Â Â Â Â Â Â Â Â  Current- voltage relationship.

Ohmâ€™s law.

• States that the current through a conductor is directly proportional to the p.d across the conductor provided that the temperature and other physical conditions remain constant.
• The physical conditions are temperature, cross- section area and length.

Â Â Â Â Â Â Â Â Â Â Â  V =IRÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â  R is set to represent the resistance of the conductor.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Resistors arrangement.

• Resistors can be arranged in a circuit in two ways
1. Series arrangement.
2. Parallel arrangement.
• The combined resistors can be calculated.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Series arrangement.

• Two or more resistors in this arrangement can be connected in series form.
• In this arrangement
1. The current through the resistors is the same.
2. Potential difference is different across each of the resistor.
• For example three resistors of resistance R1, R2 and R3 are connected in series with a cell of e.m.f V

Â Â Â Â Â Â Â Â Â Â Â  Total voltage (p.d) = VT = V1 + V2 + V3Â Â  but

Â Â Â Â Â Â Â Â Â Â Â  VT = ITRT

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  ITRT = IR1 + IR2 + IR3

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  IR = I (R1 + R2 + R3)

Â Â Â Â Â Â Â Â Â Â Â  RT = R1 + R2 + R3

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Parallel arrangement.

• Two or more resistors can be arranged in parallel.
• In this arrangement
1. The p.d across each arrangement is the same.
2. The current through each route is different.
• For example three resistors of resistance R1, R2 and R3 are connected in parallel.

Â Â Â Â Â Â Â Â Â Â Â  IT = I1 + I2 + I3Â  Â  Â  Â

• The effective resistance of the resistors in parallel is the sum of the recipricals and is less than the value of any one of them.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Types of resistors.

• Resistors are conductors specially designed to offer particular opposition to the flow of current.
• They are made from metal alloys, carbon (graphite), nichrome, tungsten, constantum, manganin.
• There are two types of resistors
1. Fixed resistors.
• Are resistors whose resistance is fixed.
1. Variable resistors.
• Are made by winding a wire (nichrome) or a piece of wood or plastic.
• The resistance can be varied e.g. rheostat vary current and potentiometer or potential divider vary p.d.
1. Non- linear resistors.
• The current passing through these resistors do not apply linearly with changes in the applied voltage. That is, they do not obey Ohmâ€™s law e.g. thermistor.
• Increase in temperature causes a decrease in resistance.
• It is used in heat operated circuits.
1. Light dependent resistors.
• Its resistance decreases when it receives light of increasing intensity.
• It is used in light operated switching circuits e.g. street lights.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Measurement of resistance.

• Resistance of a conductor can be measured using.
1. Voltmeter.ammeter method.
2. Meter- bridge method.

Voltmeter- ammeter method.

• A current is passed through the resistor and a p.d across it measured (Refer to Ohmâ€™s law experiment).

Requirement.

1. Voltmeter.
2. Ammeter.
3. Rheostat.
4. Power source.
5. Switch.
6. Conductors.
• A graph of p.d (V) against current is plotted.
• A straight line graph is obtained.
• The slope of the graph gives the resistance of the resistor.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Limitation of the experiment.

• This experiment is not accurate. That is, the resistance obtained is not accurate as the resistance used is not the one that passes through the resistor.
• The voltmeter took a little current for it to function.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Meter- bridge method.

• A more accurate method of measuring the resistance.
• Consists of resistors arranged in a bridge network, a power source and a galvanometer.
• Nichrome wire has uniform cross- section area and of high resistance.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  How it works.

1. Two resistors M and N are placed in the gaps.
2. The jockey is moved along the wire until no deflection is found on the galvanometer.
3. The bridge is said to be balanced. At balance point no current flows through the galvanometer.
4. The length L1 and L2 are recorded.
5. Since the wire is uniform, the length is directly proportional to the resistance

Â Â Â Â Â Â Â Â Â Â Â  R Â L

1. The ratio of resistance L1:L2 should be equal to the ratio of resistance M:N.

Â Â Â Â Â Â Â Â Â Â Â  Â = Â Â Â Â Â Â Â  orÂ  Â =

1. If N is the unknown resistance then

Â Â Â Â Â Â Â Â Â Â Â  N =

1. The experiment is repeated by changing M and N obtained values of L1 and L2.
2. The average of the value eliminate the errors of the experiment.

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â  Precautions.

1. The switch should be closed before the jockey touches the wire. This is necessary because of self- induction. The effect of this is that the galvanometer will deflect when the balance point is obtained.
2. A high resistance wire should be connected in series with the galvanometer to protect it from damage when the balance point is found.

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