The study of electrical circuits is essential to understand the technology that uses electricity in the real-world. This includes electricity being used for the operation of electronic devices like computers.
Aim:
In this experiment we will look at the relationship between the current going through a resistor and the potential difference (voltage) across the same resistor.
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Method:
| Voltage, | Current, |
| 1,5 | |
| 3,0 | |
| 4,5 | |
| 6,0 |
Results:
If you do not have access to the equipment necessary for the Ohm's Law experiment, you can do this activity.
| Voltage, |
Current, |
| 3,0 | 0,4 |
| 6,0 | 0,8 |
| 9,0 | 1,2 |
| 12,0 | 1,6 |
Conclusions:
An important relationship between the current, voltage and resistance in a circuit was discovered by Georg Simon Ohm and is called Ohm's Law.
The amount of electric current through a metal conductor, at a constant temperature, in a circuit is proportional to the voltage across the conductor. Mathematically, Ohm's Law is written:
Ohm's Law tells us that if a conductor is at a constant temperature, the current flowing through the conductor is proportional to the voltage across it. This means that if we plot voltage on the
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As you have seen, there is a mention of constant temperature when we talk about Ohm's Law. This is because the resistance of some conductors changes as their temperature changes. These types of conductors are called non-ohmic conductors, because they do not obey Ohm's Law. As can be expected, the conductors that obey Ohm's Law are called ohmic conductors. A light bulb is a common example of a non-ohmic conductor. Nichrome wire is an ohmic conductor.
In a light bulb, the resistance of the filament wire will increase dramatically as it warms from room temperature to operating temperature. If we increase the supply voltage in a real lamp circuit, the resulting increase in current causes the filament to increase in temperature, which increases its resistance. This effectively limits the increase in current. In this case, voltage and current do not obey Ohm's Law.
The phenomenon of resistance changing with variations in temperature is one shared by almost all metals, of which most wires are made. For most applications, these changes in resistance are small enough to be ignored. In the application of metal lamp filaments, which increase a lot in temperature (up to about 1000
In general non-ohmic conductors have plots of voltage against current that are curved, indicating that the resistance is not constant over all values of voltage and current.
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Repeat the experiment as decribed in the previous section. In this case use a light bulb as a resistor. Compare your results to the ohmic resistor.
We are now ready to see how Ohm's Law is used to analyse circuits.
Consider the circuit with an ohmic resistor,
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Ohm's law is:
which can be rearranged to:
The current flowing through the resistor is:
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The resistance of the above resistor is 10
In Grade 10, you learnt about resistors and were introduced to circuits where resistors were connected in series and circuits where resistors were connected in parallel. In a series circuit there is one path for the current to flow through. In a parallel circuit there are multiple paths for the current to flow through.
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When there is more than one resistor in a circuit, we are usually able to calculate the total combined resitance of all the resistors. The resistance of the single resistor is known as equivalent resistance.
Consider a circuit consisting of three resistors and a single cell connected in series.
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The first principle to understand about series circuits is that the amount of current is the same through any component in the circuit. This is because there is only one path for electrons to flow in a series circuit. From the way that the battery is connected, we can tell which direction the current will flow. We know that current flows from positive to negative, by convention. Current in this circuit will flow in a clockwise direction, from point A to B to C to D and back to A.
So, how do we use this knowledge to calculate the total resistance in the circuit?
We know that in a series circuit the current has to be the same in all components. So we can write:
We also know that total voltage of the circuit has to be equal to the sum of the voltages over all three resistors. So we can write:
Finally, we know that Ohm's Law has to apply for each resistor individually, which gives us:
Therefore:
However, because
, we can further simplify this to:
Further, we can write an Ohm's Law relation for the entire circuit:
Therefore:
For
Let us apply this to the following circuit.
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The resistors are in series, therefore:
Two 10 k
Two resistors are connected in series. The equivalent resistance is 100
Consider a circuit consisting of a single cell and three resistors that are connected in parallel.
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The first principle to understand about parallel circuits is that the voltage is equal across all components in the circuit. This is because there are only two sets of electrically common points in a parallel circuit, and voltage measured between sets of common points must always be the same at any given time. So, for the circuit shown, the following is true:
The second principle for a parallel circuit is that all the currents through each resistor must add up to the total current in the circuit.
Also, from applying Ohm's Law to the entire circuit, we can write:
where
We are now ready to apply Ohm's Law to each resistor, to get:
This can be also written as:
Now we have:
For
Let us apply this formula to the following circuit.
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What is the total resistance in the circuit?
Calculate the current (
Calculate the current (
Two ohmic resistors (
Real batteries are made from materials which have resistance. This means that real batteries are not just sources of potential difference (voltage), but they also possess internal resistance. If the total voltage source is referred to as the emf,
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The external resistance in the circuit is referred to as the load.
Suppose that the battery with emf
Similarly, from Ohm's Law, the voltage drop across the internal resistance is:
The voltage
The emf of a battery is essentially constant because it only depends on the chemical reaction (that converts chemical energy into electrical energy) going on inside the battery. Therefore, we can see that the voltage across the terminals of the battery is dependent on the current drawn by the load. The higher the current, the lower the voltage across the terminals, because the emf is constant. By the same reasoning, the voltage only equals the emf when the current is very small.
The maximum current that can be drawn from a battery is limited by a critical value
The maximum current that can be drawn from a battery is less than
What is the internal resistance of a battery if its emf is 12 V and the voltage drop across its terminals is 10 V when a current of 4 A flows in the circuit when it is connected across a load?
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Now that you know how to handle simple series and parallel circuits, you are ready to tackle problems like this:
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It is relatively easy to work out these kind of circuits because you use everything you have already learnt about series and parallel circuits. The only difference is that you do it in stages. In Figure 16, the circuit consists of 2 parallel portions that are then in series with 1 resistor. So, in order to work out the equivalent resistance, you start by calculating the total resistance of the parallel portions and then add up all the resistances in series. If all the resistors in Figure 16 had resistances of 10
We start by calculating the total resistance of Parallel Circuit 1.
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The value of
We can similarly calculate the total resistance of Parallel Circuit 2:
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This has now being simplified to a simple series circuit and the equivalent resistance is:
The equivalent resistance of the circuit in Figure 16 is 7,66
Determine the equivalent resistance of the following circuits:
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Another method of finding an unknown resistance is to use a Wheatstone bridge. A Wheatstone bridge is a measuring instrument that is used to measure an unknown electrical resistance by balancing two legs of a bridge circuit, one leg of which includes the unknown component. Its operation is similar to the original potentiometer except that in potentiometer circuits the meter used is a sensitive galvanometer.
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In the circuit of the Wheatstone bridge,
What is the resistance of the unknown resistor
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In addition to voltage and current, there is another measure of free electron activity in a circuit: power. Power is a measure of how rapidly a standard amount of work is done. In electric circuits, power is a function of both voltage and current:
Electrical power is calculated as:
Power (
Use Ohm's Law to show that:
is identical to
and
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| Cell | emf | Appliance for which it is designed | Current drawn from cell when connected to the appliance for which it is designed |
| D | 1,5 V | torch | 300 mA |
| AA | 1,5 V | TV remote control | 30 mA |
| What happens | Why it happens | |
| (a) | the bulb is dimmer | the AA-type cell has greater internal resistance |
| (b) | the bulb is dimmer | the AA-type cell has less internal resistance |
| (c) | the brightness of the bulb is the same | the AA-type cell has the same internal resistance |
| (d) | the bulb is brighter | the AA-type cell has less internal resistance |
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