Have you ever seen a blocked water pipe? This could be the cause of a toilet that will not flush or a sink that will not drain. To unblock the pipe you would need something that can suck the waste out, otherwise, you are stuck with a pipe full of detritus, such as food or tissue that prevents the water from flowing. But what does this have to do with electrical current? Well, it's an analogy.
The current is the flow of electrons through different cables or wires, which is like flowing water in a pipe. The rubbish in the pipe is like the resistance that resists the flow of current. In this article, we will explore the different relationships between current and resistance in different components of a circuit.
- Firstly, we will introduce the concepts of current and potential difference.
- Secondly, we shall investigate the current-potential difference graph for a resistor.
- Finally, we will explore the current-potential difference graph for a diode, filament lamp, and thermistor.
Current vs potential difference graph overview
Fig. 1 - A circuit diagram showing an ammeter connected in series and a voltmeter across a bulb in parallel.
Above, we can see a basic circuit diagram where we have a few different components. One of them is an ammeter, this component is placed within the circuit in series. An ammeter measures the current running through the circuit. This is measured in amperes (A) or milliamperes (mA) when there is a small current.
Another component is the voltmeter. This measured the potential difference (also known as voltage), which is the energy transferred to the bulb by each coulomb of charge that passes through it and needs to be positioned parallel to the component being tested. A voltmeter measures the potential difference in volts (V).
Current is the flow of charge carriers, (usually electrons) through a conducting material such as a copper wire.
Components connected in series are connected end-to-end without any branching paths. There is only a single line in which the current can flow.
Electric components connected in parallel to each other are connected by multiple paths or branches. The current can flow along each parallel path and recombine when the branches meet again.
When a charge flows steadily through an electric component we can use the following equation to calculate voltage:
\[\text{voltage}(V) = \frac{\text{energy transferred}(J)}{\text{charge}(C)}\]
Now, when electrons go through the bulb, they need to push themselves through vibrating atoms, this is what we call a resistor, whereby a circuit limits the current. Resistance is measured in ohms (Ω).
Resistance can be calculated using the following equation derived from Ohm's law:
\[resistance (Ω) = \frac{voltage (V)}{current (A)}\]
Ohm’s Law
When exploring the relationship between the current and potential difference we will see that they are directly proportional, which was seen with our equation on calculating resistance above. It also meant that resistance is constant. This idea was discovered by Georg Ohm who tested a wire at a constant temperature. It is called Ohm’s law. We performed a small experiment by applying different voltages across a fixed resistor and recording the current with an ammeter.
Voltage (\(V\)) | Current (\(mA\)) |
| 0 | 0.00 |
| 1 | 10.0 |
| 2 | 20.0 |
| 3 | 29.9 |
| 4 | 40.1 |
| 5 | 49.8 |
| 6 | 59.9 |
| 7 | 70.0 |
| 8 | 79.9 |
You can see that by applying a larger potential difference (voltage) across the resistor the current flowing in the circuit increases proportionally. Why don't you try and calculate the resistance of the circuit using ohm's law and the information above?
\begin{align*}V&=IR,\\[6pt]R&=\frac{V}{I},\\[6pt]R&=\frac{7\,\mathrm{V}}{70.0\,\mathrm{mA}},\\[6pt]R&=\frac{7\,\mathrm{V}}{7.00 \times 10^{-2}\,\mathrm{A}},\\[6pt]R&=100\,\mathrm{\Omega}.\\[6pt]\end{align*}
You can use any set of data from the table above. However, it would be easier to use a set of results without any decimal values for an easier calculation.
Current potential difference graph for a resistor
Our first graph is relatively simple. For a resistor, which is also known as an ohmic conductor, if there is a constant temperature then the current is directly proportional to the potential difference. This means if the current increases or decreases the voltage will follow the same pattern. This can be seen as there is a straight line passing through the origin of a graph. This obeys Ohm’s law.
An ohmic conductor is simply a conductor of electricity that obeys ohm's law.
A wire is an ohmic conductor because its resistance is constant even when the current changes, as long as the temperature is constant. The resistance in a metal increase with temperature because the metal atoms start vibrating faster as they have more kinetic energy. As a result, there are more collisions between the subatomic particles in the conductor. This decreases the flow of electrons and therefore the current.
Even though it might sound counterintuitive, wires actually have a very small value of resistance for their given length. This isn't by design, we would prefer our wires have no resistance at all! Unfortunately as current flows through a wire, a very small amount of energy is dissipated (wasted) as it travels and is released into the surrounding environment as heat energy. This is actually why all your electrical appliances in your home heat up when used.
There is actually a category of materials that can achieve a state of zero resistance across it, called superconductors! So why don't we use these in our electronics? Well, simply put, for a material to achieve superconductivity its temperature has to be lowered to extremely cold temperatures. Hundreds of degree celsius below zero in fact! You can understand why then we don't have superconductors in our homes.
Current potential difference graph for a thermistor
A thermistor is an electrical resistor whose resistance is greatly reduced by heating and is used for measurement and control of temperatures. Thermistors are commonly used in digital thermometers, they are commonly utilised in ovens, fridges, and even vehicles.
At low temperatures, the resistance of the thermistor is high so only a small flow of current is permitted. While at high temperatures, the resistance is small so the flow of current is greater.
Fig. 2 - Current against potential difference graph for a transistor.
A large current means more electrons are moving past an arbitrary point per second for a particular potential difference, therefore the resistance is smaller. The current is not directly proportional to the voltage when applied across a thermistor and this is why the graph is curved.
Current potential difference graph for a diode
Fig. 3 - Current against potential difference graph for a diode.
The current potential difference graph for a diode is quite different when compared to a graph for a resistor. Firstly, a diode is a component in a circuit which allows current to flow in a specific direction. If the current is in the direction of the arrowhead symbol this is known as forward bias, causing a sharp increase in voltage and current as seen on the right side of the graph.
When a diode is turned the other way, it no longer conducts electricity and this is known as reverse bias, this is presented on the left side of a graph. A diode has to surpass a voltage (typically around 0.6V), which is known as a threshold in order to start conducting electricity. Diodes do not obey Ohm's law. They are typically used in communications equipment and logic gates for computers but have many more applications too.
Current potential difference graph for a filament lamp
In a filament lamp the current increases at a slow rate when compared to the potential difference. This happens because when more current passes through the filament lamp, its temperature increases. As the filament in the bulb is metal, the resistance of the component also increases with increasing temperatures.
Fig. 4 - Current against potential difference graph for a lamp filament.
Now, resistance acts to oppose the current which is why the rate of change of current relative to the voltage slows down significantly at higher potential differences. There are parts in the graph where there are straight lines, this means the resistance is constant. When the resistance changes then the graph curves. Filament lamps do not obey ohm's law.
Current vs potential difference graph example
Let us go through some example questions to consolidate our knowledge.
You could be asked to draw and analyse some of these graphs, so it is important that you are familiar with them.
Question
The energy transfer to a bulb is 320J when 60.0C of charge pass through it. What is the potential difference?
Solution
First, let us look at what information we have available.
We have the energy transferred which is 320J and the charge which is 60.0C. So to find the potential difference we can use the following equation.
\[\text{voltage (V)} = \text{energy transferred (J)} \div \text{ charge (C)}\]
So now all we need to do is plug our numbers in:
\[\text{voltage (V)} = 320\text{ J}\div 60.0\text{ C}\] \[\text{voltage (V)} = 5.33\text{ V}\]
So the potential difference is 5.33 V.
Question
Explain why resistance in a metal increases with temperature.
Solution
The resistance in a metal increases with temperature because the metal atoms start vibrating faster as they have more kinetic energy. As a result, there are more collisions between the conduction of the electrons and atoms.
Question
Explain how would be a sketch of a current potential difference graph for a resistor.
Solution
On the x-axis is the potential difference in volts (V) and on the y-axis is the current in amps (A). For a resistor, the current and potential difference are directly proportional so there is a straight line going through the origin.
Current Potential Difference Graph - Key takeaways
- Potential difference can be calculated by \(\text{voltage (V)} = \text{energy transferred (J)} \div \text{charge (C)}\)
- Resistance can be calculated by \(\text{resistance (Ω)} = \text{voltage (V)} \div \text{current (A)}\)
- Ohm’s law is that the potential difference and current are directly proportional in resistors at a constant temperature.
- Diodes and filament lamps do not obey Ohm’s law.
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