__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 Ohm’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 Ohm’s law. Resistance in series and in parallel.

__Electric current.__

- Electricity – is the effect of electric charges.
- Static electricity – is electricity produced by static charges.
- Electrostatic – is the study of effect of electric charges.
- Dynamic electricity – 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;

- Alternating current (a.c)
- Direct current (d.c)

__Electric current.__

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

Q = It

- Is measured in amperes using an ammeter

1 Q = 6.25 x 10^{18}

__Electric circuit.__

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

__Cell.__

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

__Types of cell.__

__Open circuit.__

- This is a circuit where charges do not flow.

__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.

__Short circuit.__

- Is a circuit where a conductor is used to make current bypass an appliance.

** 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).

** Potential difference**.

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

p.d = E/Q =E/It but E/t = power

p.d =power/amperes =w/a

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

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.

- Electromagnetic force (e.m.f)
- 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 cell’s terminal when the cell is not connected to an external circuit.
- It is measured in volts.

** Internal resistance**.

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

__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.

__Factors affecting resistance.__

__Length .__

- A conductor’s ability to resist the flow of current is directly proportional to the length.
- A longer conductor has a high resistance.

__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.

**Material.**

- Good conductors e.g. silver, copper and aluminium have low resistance or no resistance than bad conductors.

**Temperature.**

- The conductor’s resistance is directly proportional to temperature.

__Resistivity.__

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

R

R = Pl/A

P =RA/L = where P is a constant SI unit = ɲm

__Current- voltage relationship.__

**Ohm’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.

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

__Resistors arrangement.__

- Resistors can be arranged in a circuit in two ways

- Series arrangement.
- Parallel arrangement.

- The combined resistors can be calculated.

__Series arrangement.__

- Two or more resistors in this arrangement can be connected in series form.
- In this arrangement

- The current through the resistors is the same.
- Potential difference is different across each of the resistor.

- For example three resistors of resistance R
_{1}, R_{2}and R_{3}are connected in series with a cell of e.m.f V

Total voltage (p.d) = V_{T} = V_{1} + V_{2} + V_{3} but

V_{T} = I_{T}R_{T}

_{ }I_{T}R_{T = }IR_{1} + IR_{2 }+ IR_{3}

_{ }IR = I (R_{1} + R_{2 }+ R_{3})

R_{T} = R_{1} + R_{2} + R_{3}

__Parallel arrangement.__

- Two or more resistors can be arranged in parallel.
- In this arrangement

- The p.d across each arrangement is the same.
- The current through each route is different.

- For example three resistors of resistance R
_{1}, R_{2}and R_{3}are connected in parallel.

I_{T} = I_{1 }+ I_{2} + I_{3}

- 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.

__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

__Fixed resistors.__

- Are resistors whose resistance is fixed.

__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.

__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 Ohm’s law e.g. thermistor.
- Increase in temperature causes a decrease in resistance.
- It is used in heat operated circuits.

__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.

__Measurement of resistance.__

- Resistance of a conductor can be measured using.

- Voltmeter.ammeter method.
- Meter- bridge method.

__Voltmeter- ammeter method.__

- A current is passed through the resistor and a p.d across it measured (Refer to Ohm’s law experiment).

__Requirement.__

- Voltmeter.
- Ammeter.
- Rheostat.
- Power source.
- Switch.
- 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.

__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.

__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.

__How it works.__

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

R L

- The ratio of resistance L
_{1}:L_{2}should be equal to the ratio of resistance M:N.

= or =

- If N is the unknown resistance then

N =

- The experiment is repeated by changing M and N obtained values of L
_{1}and L_{2}. - The average of the value eliminate the errors of the experiment.

__Precautions.__

- 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.
- 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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