Electical Engineering Experiment

EXPERIMENT NO. EE100L – 03

SERIES AND PARALLEL EQUIVALENT RESISTANCES

1. OBJECTIVES:

1. To calculate the single resistance which is equivalent to a group of resistors connected in series.
2. To calculate the single resistance which is equivalent to a group of resistors connected in parallel.

1. DISCUSSIONS:

All materials possess electrical resistance, (opposition to the flow of electric current) to a greater or lesser degree. Materials such as silver, copper and aluminum, which have relatively low resistance, are such called conductors, while materials such as plastics, glass, air and rubber, which have high resistance are called insulators. Between these two major categories are a great variety of materials and alloys which have neither very high nor very low resistance (“or resistivity”). There is no clear cut division line between conductors and insulators. Conductors gradually merge into resistors and resistors gradually merge into insulators. A material has low electrical resistance when it offers little opposition to the passage of an electric current. The unit of the electrical resistance is the ohm.

RESISTORS IN SERIES

When a group of resistors is connected in series, the total resistance is equal to the sum of the values of resistors. Thus, if a resistor, having a resistance of 5 ohms is connected in series with one having a resistance of 20 ohms, (see Fig. 1) the total resistance between terminals A and B is 25 ohms.

[pic 1]

The two resistors (R1 and R2) between terminals A and B could be replaced by a single resistor (R3) having a resistance of 25 ohms. This single resistor (R3) which can replace the original two is called the equivalent resistance. See Fig. 2

[pic 2]

The equivalent resistance of a number of resistors in series is found from the equation:

Requivalent = R1 + R2 + R3 + …

RESISTORS IN PARALLEL

When two or more resistors are connected in parallel between two terminals A and B, the resultant resistance is always less than that of the lowest resistor. The logic of this statement can be shown by referring to Fig. 3.

[pic 3]

In this circuit, a resistor of 5 ohms (R1) is initially connected between terminals A and B. In another resistor of 20 ohms (R2) is connected in parallel with the 5 ohm resistor (R1), it is clear that the opposition to the current flow between A and B will be less than before. This is because the current has an additional path to flow through which is not available when the 5 ohm resistor (R1) was alone in the circuit. The equivalent resistance of a number of resistors in parallel is found from the equation:

1/Requivalent = 1/R1 + 1/R2 + 1/R3 + …

For the particular case where only two resistors are in parallel, the single equivalent resistance can be found from the equation:

Requivalent = (R1 x  R2) / (R1 + R2)

The equivalent resistance of 20 ohms in parallel with 5 ohms is therefore:

(5 x 20) / (5 + 20) = 4 ohms

Consequently, a single resistor of 4 ohms (R3) can be used to replace the original two. See Fig. 4

[pic 4]

1. INSTRUMENTS AND COMPONENTS

None

1. PROCEDURE

1. Using the equations given in the DISCUSSION section, calculate the value of the single equivalent resistance between terminal A and B of the following series and parallel circuits. Show your calculations in the spaces provided.

[pic 5]

1. Requivalent = 600 Ω

1. Requivalent = 900 Ω

1. Requivalent = 2100Ω

1. Requivalent = 1100Ω

1. Requivalent = 2100 Ω

[pic 6]

1. Requivalent = 300 Ω

[pic 7]

1. Requivalent = 200 Ω

1. Requivalent = 240 Ω

1. Requivalent = 150 Ω

1. Requivalent = 171.43 Ω

[pic 8]

1. Requivalent = 200 Ω

1. Requivalent = 133.33 Ω

1. Requivalent = 32.31Ω

1. Requivalent = 100Ω

1. Requivalent = 120 Ω

1. TEST YOUR KNOWLEDGE

1. The terms “open circuit”, “short circuit” and “dead short” are used in speaking electricity. Can you answer the following questions about these three terms?

1. What is the value of the resistance of an open circuit?

        The value of resistance is so high it can be considered infinite.