Tutorial 2 - Measurements from Simple Circuits

In Tutorial 1 we saw that there were two main electrical measurements we could make easily:

• Voltage - this is done with a voltmeter;
• Current - this is done with an ammeter.

We use voltmeters and ammeters in circuits, in that the ammeter is wired in series with the component, while the voltmeter is wired in parallel.

We usually treat ammeters and voltmeters as perfect:

• A perfect voltmeter has an infinite resistance so takes no current.

• A perfect ammeter has zero resistance.  Therefore there is no voltage drop across it.

However, real voltmeters and ammeters are not perfect.

Voltmeters

Real voltmeters have a high (but not infinite) resistance and are connected across the component.  The meter on the left is an analogue instrument.  It has a needle and a scale.  It also has quite a low resistance, which means that it will not measure the voltage across high value resistors accurately.

Picture by Hannes Grobe, Wikimedia Commons                                         Picture by Ravn, Wikimedia Commons

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A digital voltmeter is shown in the picture on the right.   Digital voltmeters have a very high resistance, about 107 W (10 000 000 W  or 10 Megohms), which makes them almost perfect.  The picture shows a commercial digital voltmeter, with a home-made instrument built by students of the Technical University of Berlin.

Whatever the type of instrument, it is vital that the range selected is appropriate to the voltage measured.  The picture below shows the mess that can be made when a 30 volt instrument was connected to a 230 V supply.  One of the multiplier resistors has completely blown apart.

Picture by Daan Berg, Wikimedia Commons

Ammeters

Ammeters have a very low value of, but quite definite, resistance.   The meter has a very low value resistor called a shunt wired in parallel.

Many schools and colleges buy analogue meters that can be turned into voltmeters, ammeters, or ac meters by plugging appropriate multipliers and shunts onto the instrument.

When you use a meter like this, you need to know what voltages or currents you are using.  It would be no good measuring a current of 50 mA (milliamps) using the 10 A shunt.  If you were measuring a voltage of 30 V, you would use the 50 V range on the multiplier.  You also need to read the correct scale.  If you are using the 50 V range on the multiplier, you need to use the bottom scale.  A needle deflection to 1 would be 10 V.

If you use the 10 A range on the shunt, 6 on the top scale will be 6 A.  However, if you were using the 2 A range, you need to have to multiply the top scale by 0.2 - if you have a reading of 6 on the top scale, the current is 6 × 0.2 = 1.2 A.

Multimeters

The Multimeter is a combined instrument that can:

• Measure voltage

• Measure current

• Measure resistance

• Measure frequency in some instruments.

• Test diodes and transistors in some instruments.

1. Function/Range Switch: selects the function (voltmeter, ammeter, or ohmmeter) and the range for the measurement.

2. COM Input Terminal:Common ground, used in ALL measurements.

3. V Input Terminal: for voltage or resistance measurements.

4. 200 mA Input Terminal: for small current measurements.

5. 10 A Input Terminal: for large current measurements.

6. Low Battery LCD: appears when the battery needs replacement.

There may be an internal fuse or a cut out to prevent excessive currents in ammeter mode, which otherwise might damage the instrument.

The digital multimeter is very close to being a perfect voltmeter, with a very high input resistance, with a very low input current.

Digital multimeters have functions with which they can test capacitors, diodes, and transistors.  They can also display frequency.

 Question 1 Do the matching exercise Question 2 Multiple choice question on ammeter Question 3 Multiple choice question on meters

Further Electrical Quantities

Having measured the voltage and the current, we can work out other quantities that are of interest to the electrical and electronic engineer:

• Power.  Power is the rate at which electrical energy is turned to other kinds of energy.  Power is the voltage multiplied by the current.

• Resistance.  Resistance is the amount by which a conductor opposes the flow of current.  Resistance is the voltage divided by the current.

• Conductance.  Conductance is the amount by which a conductor allows current to flow.  Conductance is the current divided by the voltage.

There is another quantity that is of more interest to the physicist, charge.  Charge is the current multiplied by the time.

Power in a Circuit

Power in a circuit can be worked out using the simple relationship:

Power (W) = Voltage (V) × Current (A)

In physics code, this is written:

P = IV

The physics code for current is I which stands for "intensité du courant", the French phrase meaning "intensity of the current".

Power is measured in watts (W).  Remember:

• 1 mW = 1 × 10-3 W

• 1 kW = 1000W

• 1MW = 1 × 106 W

In electronic circuits the power may be low, say ½ watt.  However if the resistors are rated at ¼ watt, they will start to get hot.

 Worked example A current of 2.0 mA is flowing at a voltage of 12 volts.  What is the power that is transferred? Answer P = VI = 2.0 × 10-3 A × 12 V = 24 × 10-3 W = 0.024 W

This power is well within the capacity of a ¼ watt resistor.

 Question 4 Answer the interactive question on power.

Resistance

Resistance is the opposition to the flow of an electric current.  In physics, it is defined as the ratio of the voltage to the current.

Resistance (W) =Potential difference (V)

Current (A)

In Physics code:

R = V/I

The formula is often referred to the Ohm's Law Equation.  Ohm's Law states that:

the potential difference across the ends of a conductor is directly proportional to the current flowing through the conductor, provided that temperature and other physical conditions remain the same.

The unit for resistance is ohm (W).  (The curious symbol ‘W’ is Omega, a Greek capital letter long Ō.)  There are some very important multipliers:

• kilohms (kW): 1 kW = 1000 W

• megohms (MW): 1 MW = 1 × 106 W

In some schematics, you will see the letter R for ohms, and k for kilohms.  22 R stands for 22 W;  22 M = 22 × 106 W

 Worked example A current of 2.0 mA is flowing at a voltage of 12 volts.  What is the resistance of the component? Answer R = V/I = 12 V ÷ 2.0 × 10-3 A = 6000 W = 6 kW

You must be able to recognise and use the multipliers for resistance.

 Question 5 Answer the interactive question on resistance.

Conductance

The reciprocal of resistance is called conductance, which is used by some electrical engineers in the power industry.  When wires have very low resistance, it is reasonable to say that they have a high conductance.  Conductance is given the physics code G and has the formula:

In terms of resistance we write:

The units for conductance are Siemens (S), although in some books and magazine articles, you may see it written as mho (Ohm written backwards.  Get it?).

The Heating Effect of a Current

We can combine the equations for resistance and power to give these two equations for power:

P = I2R or P = V2/R

Power is in Watts (W) or kilowatts (kW) or milliwatts (mW)

 Worked example A current of 2.0 mA is flowing through a 50kW resistor.  What is the power? Answer P = I2R =  (2.0 × 10-3 A)2 × 50 000 W = 0.2 W = 200 mW

 Question 3 A 300 ohm resistor is rated at ½ watt.  It is connected to a 20 V supply.  What is the power supplied? What will happen to the resistor?

This equation is important.  If a resistor has to dissipate more heat than its rating, it will get hot.  The pictures below shows what happens when a 33 ohm resistor rated at 1 watt is connected to a 20 volt supply.  It was dissipating 12 watts.

It doesn't take a genius to see the danger of this situation.  Using high power resistors will prevent this kind of thing happening.  You can get resistors rated at 5 W, 10 W, etc.  Carbon-film resistors are the cheapest, but have low power ratings.  High power resistors are more expensive than carbon film, as they are made of resistance wire wound onto a former.