These are samples of learning materials and may not necessarily be exactly the same as those in the actual course. Contents 1.

Transcription

1 Contents These are samples of learning materials and may not necessarily be exactly the same as those in the actual course. Contents 1 Introduction 2 Ohm s law relationships 3 The Ohm s law equation 4 Calculating circuit current 6 Calculating resistance 7 Current direction and voltage polarity 8 Meter connection and use 10 Measuring voltage 10 Measuring current 11 Measuring voltage and current simultaneously 12 Connecting to the circuit 12 Range setup 13 Reading analogue scales 13 Zero adjust 17 Digital meters 19 Meter selection 20 Analogue versus digital meters 20 Multimeters 21 Summary 24 Answers 25 1

2 Introduction Ohm's Law states the relationship between the voltage across a resistor, the current through a resistor and resistance. Ohm s law allows us to perform calculations to determine any one of current, voltage, or resistance from the other two. Ohm s Law is the most extensively used equation in electrical theory. After completing this topic, you should be able to: state the relationship between voltage and current from measured values in a simple circuit calculate the voltage, current or resistance in a circuit given any two of these quantities interpret and draw graphs to show relationships of voltage, current, and resistance explain the relationship between voltage, current and resistance. 2

3 Ohm s law relationships In an electrical circuit, there is a definite relationship between current, voltage and resistance that was discovered by Georg Ohm. He expressed the relationships in written form, which became known as Ohm s law. In a circuit with a constant resistance, any increase in the applied voltage will cause a proportional increase in current. This means for example that: doubling the voltage doubles the current, halving the voltage halves the current, quartering the voltage quarters the current, and so on. This relationship is one of direct proportion and can be written as: I E Read this as current is proportional to emf Now if we maintain a constant supply voltage and vary the circuit resistance, the circuit current changes in inverse proportion. That is: doubling the resistance halves the current, halving the resistance doubles the current, quartering the resistance increase current four times, and so on. This relationship is one of inverse proportion and can be written as: 1 I R Read this as current is inversely proportional to resistance 3

4 The Ohm s law equation Ohm s Law states that the current flowing through a resistance is: directly proportional to the potential difference between them inversely proportional to the resistance. Ohm s law may be written as: where: V = voltage (volt) R = resistance (ohm) I = current (ampere) Written as shown above, the Ohms Law equation expresses the current resulting from a particular voltage (V) and resistance (R). But you will just as often be given current (I) and resistance (R) and asked to find voltage (V). Or you may be given current (I) and voltage (V) and asked to find resistance (R). Transposing to find R Start with the basic equation: Multiply both sides of the equation by R: R I = V R R The letter R cancels on right hand side of the equation giving: I R = V Divide both sides by I: R I V = I I The letter I cancels on left hand side of equation giving: R = V I 4

5 Transposing to find V Start with the basic equation: Multiply both sides of the equation by R: I R = V R R Cancel Rs on right hand side: I R = V Usually it is expressed as: V = IR We have three forms for the Ohm's Law relation: R = V I V = IR Note that in any of these forms, the voltage (V) may also be an emf (E). 5

6 Calculating circuit current Let's use the Ohm's Law equation to calculate current from voltage and resistance. You may need to do this for example before you connect a circuit, to check that the current will remain within safe limits. Example 1 Determine the current in a 5 Ω resistor when 12 V is applied. Given R = 5 Ω V = 12 V I =? = 12 5 = 2.4 A Note: Always express answer as a decimal, not a fraction. Example 2 If the voltage in Example 2 is reduced to 8 V, find the new current value. Given R = 5 Ω V = 8 V I =? = 8 5 = 1.6 A 6

7 Calculating resistance Example 3 A current of 6 A flows in a 10 Ω resistor when connected to a 60 V supply. What resistance will reduce the circuit current to 5 A? Given V = 60 V I = 5 A R =? R = V I = 60 5 = 12 Ω Example 4 A variable resistor can have its resistance varied to control the current in a circuit with a 120 V supply. If the current is to be varied from 25 A to 8 A, what must be the variation in resistance in the variable resistor? Given V = 120 V I max = 25 A or I 1 = 25 A I min = 8 A or I 2 = 8 A R =? (variation) R = V 1 2 I 1 = = 4.8 Ω R = V I 2 = = 15 Ω Therefore the variation in resistance of the variable resistor is from 4.8 Ω to 15 Ω. 7

8 Check your progress 1 Using Ohm s law, fill in the blanks in the table below. Voltage (V) volt Current (I) ampere Resistance (R) ohm 30 V 3 kω 40 m A 600 Ω 4.8 m A 2.2 Ω 12 V 330 µ A 20 V 12 M Ω 10 V 10 A 2 Calculate the resistance of the lamp in the following circuit. 3 A 24 Ω heating element requires a current of 10 A to produce its specified heat output. Calculate the required supply voltage for this heater. 22

9 4 Calculate the resistance of a resistor that takes 100 ma when connected to a 10 V battery. 5 Calculate the voltage across a 4.7 kω resistor that has 3.5 A passing through it. 6 In what way does a digital multimeter differ from an analogue multimeter when using it to measure current? 7 Give one advantage of a digital multimeter compared to an analogue multimeter. 8 Give one disadvantage of a digital multimeter compared to an analogue multimeter. 9 Briefly explain why an analogue meter must be viewed straight on. 10 Briefly explain how to zero an analogue ohmmeter. 11 Explain why it is important to set the multimeter to its highest range, especially when measuring an unknown voltage. Check your answers with those given at the end of the section. 23

10 Summary Ohm s law states that the current in any circuit, or part of a circuit, is directly proportional to the voltage and inversely proportional to the resistance, that is: The three equations obtainable from Ohm s Law and its transpositions are: V = IR An ammeter is an instrument used for measuring electrical R = V I current flow in a circuit. A voltmeter is an instrument used for measuring electrical voltage between two points in a circuit. A multimeter is a multi-purpose meter that can measure voltage, current and resistance and has a series of ranges for each function. Ammeters, voltmeters and multimeters are available in analogue and digital versions. Voltmeters should have as high a resistance as possible, and ammeters as low a resistance as possible. 24

11 Answers Activity 1 1 Ohm's law 2 = 10 2 = 5 A 3 The current is halved. 4 The current is increased by a factor of 4 that is, quadrupled. 5 At minimum resistance, R = 15 Ω and so = = 10 A At maximum resistance R = 45 Ω and so = = 3.33 A Therefore the current variation is 3.33 to 10 A. Activity 2 1 Resistance parallel. 2 Ammeter resistance. 3 25