Current electricity is the rate at which an electricity source will make charges to flow or pass a certain point in a conductor or in an electric circuit.

This means that, when electrical devices Electric current is the rate of charge flow past a given point in an electric circuit, measured in Coulombs/second which is named Amperes. In most DC electric circuits, it can be assumed that the resistance to current flow is a constant so that the current in the circuit is related to voltage and resistance by Ohm's law. The standard abbreviations for the units are 1 A = 1C/s.

COMBINATION OF RESISTORS

Resistors can be connected either in series or parallel depending on the magnitude of effective resistance required. Series connection gives a bigger value of effective resistance and the parallel connection gives small value of effective resistance.

RESISTORS IN SERIES

By connecting resistors in series, when the switch 'S' is closed, the current 'I' which flows through the circuit flows through each resistor.

Total resistance between points A and B which is commonly referred to as equivalent resistance (Req) will produce a potential difference in the circuit given by ohm’s law as;

V=IReq

The voltage across each resistor in the circuit is given by V1 =IR1 and V2 =IR2

The sum of the voltage drops equal to the potential difference in the circuit (i.e. potential difference between (A and B)

Total voltage = V1 + V2

... VT = V1 + V2

Total voltage = V1 + V2

Since V = IR, V1 = IR1 and V2 = IR2

IRT = IR1 + IR2

IRT =I (R1 + R2 )

RT = R1 + R2

RESISTORS IN PARALLEL

RESISTORS IN PARALLEL

In the figure below I is the current in the main circuit. On the other hand I1 and I2 are current through individual resistors R1 and R2.

The sum of all currents through the resistors which are connected in parallel gives the value of current equal to the main circuit.

.

.

Therefore, IT = I1 + I2

If RT is the equivalent resistance of the main circuit between A and B, then by Ohm’s law the current is given by;

From IT = I1 + I2

On diving both sides by V

On diving both sides by V

Cross multiplication

1(R1R2) = RT (R1 + R2)

For two resistors connected in parallel.

EXAMPLES

1.Given that R1= 4Î© and R2= 6Î©, find the equivalent resistance when the resistors are connected.

1.Given that R1= 4Î© and R2= 6Î©, find the equivalent resistance when the resistors are connected.

- In parallel

2. In series

Solution

1.Series

Solution

1.Series

RT = R1+R2

RT = 4Î© + 6Î©

RT = 10Î©

2.Parallel

2.Parallel

= 2.4Î©

2.Two conductors of resistance 4Î© and 5Î© are connected in series across a 60V supply. Find;

2.Two conductors of resistance 4Î© and 5Î© are connected in series across a 60V supply. Find;

- The total resistance
- The current in the circuit
- The potential difference across each resistor

RT = R1+R2

= 4Î© + 5Î©

= 9Î©

the total resistance = 9Î©

the total resistance = 9Î©

I = 6.7A

Potential difference across R1

Potential difference across R1

V1 = IR1

V1 = 6.7 x 4 = 26.8v

Potential difference across R2

V2 = IR2

V2 = 6.7 x 5 = 33.5v

Total current = 26.8 + 33.5 = 60A

3.Consider the circuit shown below. What will be the reading on the Ammeter?

Solution

V = 12V

RT =2Î©

I = 6A

EXERCISE

1. In a circuit, the amount of charges passing through a point is 9 coulombs in 4.5 seconds. What is the electric current passing at that point?

1. In a circuit, the amount of charges passing through a point is 9 coulombs in 4.5 seconds. What is the electric current passing at that point?

Solution

Quantity of charges = 9 coulombs

Time = 4.5 sec

Electric current =?

Electric current = 2coulombs/sec

2. The two resistances 15Î© and 5Î© are connected in series across 20v supply, find;

2. The two resistances 15Î© and 5Î© are connected in series across 20v supply, find;

- Total resistance
- The total current in the circuit
- The current through each resistor

Solution

Data given

R1 = 15Î©

R2 = 5Î©

Voltage = 20v

The total resistance

The total resistance

RT = R1 + R2

= 15Î© + 5Î©

= 20Î©

The total current in a circuit (I)

The total current in a circuit (I)

From V = IR

But v = 20v, R = 20Î©

I = 1A

The current through each resistor

But V = 20V, R1 =15Î©

= 1.3A

but V = 20 V, R = 5Î©

but V = 20 V, R = 5Î©

I2 = 4A

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