SITEMAP School Physics Notes: Electricity 3.1 Ohm's Law investigation I=V/R calculations

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Electricity Section 3: 3.1 Ohm's Law and electrical resistance of a wire - circuit to measure current and voltage to calculate resistance - what is an ohmic conductor?

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ANSWERS to ALL the QUESTIONS at the end of the page

3.1A Ohm's Law

(and a mention of other units dealt with in other sections)

Questions to be answered: What is Ohm's Law? How do you do calculations using Ohm/s Law? How do you construct and use a circuit to investigate Ohm's Law? i.e. how to investigate the variation of current in a circuit when the p.d. ('voltage') is varied.

Ohm's law states that the current (I in A) passing through a conductor between two points, is directly proportional to the voltage (potential difference, p.d. in V) across the two points in a circuit, and, inversely proportional to the resistance (in ohms, Ω).

It involves a most fundamental equation you need to know for electricity calculations.

This can be expressed mathematically as: I = V / R

rearrangements: V = IR   and   R = V/I  (better than using formula triangle!)

I = current in amperes, amps, A; a measure of the rate of flow of electric charge.

V = potential difference, p.d., volts, V; a measure of the potential energy given to the electric charge flowing.

The potential difference in a circuit is the energy transferred per coulomb of electric charge that flows between two points in an electric circuit.

The coulomb (C) is the unit of electric charge (see equation notes). LINK

The energy transferred is calculated from the p.d. and the quantity of electric charge (Q) moved by the p.d. in V (see E = QV equation notes).. LINK

R = resistance of the wire, ohms, Ω; a measure of the ability of a conductor to inhibit the flow of charge.

The greater the resistance of a resistor, the more it resists and slows down the flow of electricity.

Ohm's law means that the R in this equation is a constant, independent of the size of the electrical current flowing.

The law correctly applies to so-called ohmic conductors, where the current flowing is directly proportional to the applied potential difference, but some resistors don't obey this law e.g. the heated filament of a light bulb. The basic circuit in the context of investigating Ohm's law. 3.1B A simple experiment to measure the resistance of a single component with multiple voltage-current readings

If you set up circuit 31 (right diagram) you can measure the resistance of the fixed resistor [R].

By varying the voltage from the power supply using the variable resistor you can readily get lots of pairs of readings of p.d. (V) and current (A).

Then use Ohm's Law equation R = V/I to calculate the value of the fixed resistance - examples of calculations below.

You can then average the values of R calculated for a more reliable result. This is the basic set-up to investigate the current-voltage characteristics of any component R.

A voltmeter is always wired in parallel with the resistor.

Examples of calculations using Ohm's Law equation

Q1 When a p.d. of 4.5 V is applied across a resistor, a current of 0.5 A flows.

What is the resistance of the device?

Q2 A resistance has a value of 50 ohms.

What p.d. must be applied across it to cause a current of 5.0 A to flow through it?

Q3 A p.d. of 240 volts is applied across a heating element resistor of 30 ohms.

How much current flows through the heater?

Q4 Three 1.5 volt batteries were wired in series with three bulbs.

If the ammeter measured a current of 0.50 A, what is the resistance of each bulb?

3.1C Investigating the current - voltage characteristics of a wire

This is an Ohm's Law experiment Circuit 31 shows you how to investigate how I varies with V for a resistance

The investigation is all about finding out ...

... how does the current flowing through a resistor vary with the potential difference across it?

The fixed resistor represents a 'component' in a circuit and must be at constant temperature throughout the experiment (see later on temperature effect in a metal filament bulb).

In this case a simple wire resistor is wired in series with the power supply and ammeter.

A voltmeter is always wired in parallel with the resistor or any other device being investigated.

The p.d. is measured across the fixed resistance with the voltmeter, However, also wired in series, a variable resistor is added, so that you can conveniently change the potential difference and thereby change the current flowing through the component.

This allows you to gather a whole series of pairs of I and V readings, with which to plot suitable graphs - in this case of V versus I, but often done as I versus V.

Using the variable resistor, you gradually increase the potential difference across the component, taking the matching current reading e.g. increasing at 0.5 V at a time. Repeat each reading twice and use the average.

You can then swap the battery terminals and repeat all the readings.

If you plot the p.d. versus current, the graph is linear if it obeys Ohm's Law - it is then called an 'ohmic conductor'.

This I've represented by the graph above on the right, and the gradient is equal to the resistance in ohms.

This corresponds to the Ohm's Law equation V = IR, so the gradient is R.

If the graph remains linear, the resistance is remaining constant.

This graph does not represent the readings taken after reversing the battery terminals.

However, it does show how to get the value of a resistance by a graphical method.

Its a linear graph and the phrase linear component may be used. For components like a wire that doesn't heat up, you should get a linear plot of p.d. (V) versus I (A) with a gradient R (Ω). (right graph).

You should make sure that the wire doesn't heat up too much - if it starts getting warm, immediately disconnect the resistor ('switch off') and let it cool down. If you plot I versus V the gradient is 1/R (the reciprocal of the resistance), linear graph.

This graph shows what you get by plotting all the data, including the I-V readings taken after reversing the battery terminals.

The graph (1) is constructed on a crosswire axis. The top right half is your first set of results, you then reverse the terminals on the power supply and repeat the experiment giving the bottom left part of the graph.

Note that you will only get a linear graph if the temperature of the wire remains constant.

When the current (A) is proportional to the p.d (V) it is described as an ohmic conductor (obeys Ohm's Law!).

Using the circuit 31 you can test any resistor or any other type of circuit component and the results are discussed below starting with a summary of factors that affect resistance. So,  the resistance of an ohmic conductor e.g. a circuit component doesn't change no matter current is passed through - constant gradient of 1/R for graph 1. Current versus voltage graphs for different wire resistances.

These are the expected linear graphs for a fixed resistor using circuit 31 above.

Thinking anti-clockwise on the diagram, the different graph lines might depict a decreasing resistance e.g. (i) a resistance wire getting shorter for the same diameter, or (ii) the diameter getting larger for a fixed length of wire.

At a constant temperature the current flowing through an ohmic conductor is directly proportional to the potential difference across it - the equation is V = IR or I = V/R.

However, this is only true, giving a linear graph if the temperature doesn't change. Current is always determined by a combination of the p.d. (V) and the resistance R (Ω).

The independent variable is what we change or control in the experiment - in this case you can consider it as the p.d. controlled by the variable resistor.

One convention is to plot the independent variable on the x-axis, and the dependent variable on the y-axis. This means the resistance R, is the reciprocal of the gradient - a bit more awkward to calculate the resistance than from the V versus I graph plot, where the gradient is the resistance.

Ohm's Law: I = V / R.

The dependent variable is what we are testing or measuring in the experiment, this is the current I (A), which depends on the variable resistor setting, which in turn controls the potential difference across the resistor.

The control variables are what we keep the same during the experiment to make sure it’s a fair test e.g. in this case the wire and temperature are kept constant, should NOT be varied - don't change the wire or allow the wire to heat up.

3.1D Electrical resistance - experiments to investigate the I-V characteristic of various resistances and the validity, or otherwise, of Ohm's Law

What affects the resistance of a wire? Is resistance constant? and some characteristic current-voltage graphs (I-V plots) explained in Parts 3.2 to 3.4 (via index)

The resistance of a circuit depends on several factors:

(i) the thickness of the resistance wire - for a single component resistor

(ii) the length of the resistance wire - for a single component resistor

(iii) if more than one resistance, are they wire in series or parallel?

(iv) the temperature of a component that acts as a resistance

These are looked at further in Parts 3.2 to 3.4 (links below)

3.3 Investigating current - voltage characteristics of a metal filament lamp - graph explained

3.4 Investigating the current - voltage characteristics of a diode - graph explained Parts 3.2 to 3.4 describe and explain several examples of I-V graphs - which can be investigated using circuit 31 (on the right)

The circuit diagram 31 on the right shows how you can investigate the variation of current through a resistance (or any component) when you vary the potential difference.

Current–potential difference graphs are used to show how the current through a component varies with the potential difference across it.

The resistance of some resistors/components does change as the current and p.d. changes e.g. a diode or filament lamp.

Keywords, phrases and learning objectives for Ohm's Law in electricity

Know how to explaining Ohm's Law and electrical resistance and use the formula in calculations.

Be able to describe the circuit and method used to measure the variation of current with p.d. (voltage) to calculate resistance.

Be able to use and rearrange the formulae I = V/R V=IR R = V/I to solve problem involving calculations relating current, p.d. voltage and resistance for an ohmic conductor.

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ANSWERS to the examples of calculations using Ohm's Law V = IR

Q1 When a p.d. of 4.5 V is applied across a resistance, a current of 0.5 A flows.

What is the value of the resistor?

R = V/I = 4.5/0.5 = 9.0 Ω

Q2 A resistance has a value of 50 ohms.

What p.d. must be applied across it to cause a current of 5.0 A to flow through it?

V = IR = 5 x 50 = 250 V

Q3 A p.d. of 240 volts is applied across a heating element resistor of 30 ohms.

How much current flows through the heater?

I = V/R = 240/30 = 8.0 A

Q4 Three 1.5 volt batteries were wired in series with three bulbs.

If the ammeter measured a current of 0.50 A, what is the resistance of each bulb?

I = V / R, so R = V / I = (3 x 1.5) / 0.50 = 9.0 Ω

Since total resistance = sum of resistances, resistance of each bulb = 9.0 / 3 = 3.0 Ω

(Note that resistances wired in series can be added together to give the total resistance.)

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