Did you know that electrical circuits are ubiquitous in our everyday lives? From simple wiring on the switch of a light bulb to the complex integrated circuits that control the device that you are using, electrical circuits are everywhere around us.
By learning more about how circuits work, we can dive deeper into the key physics concepts that surround the topic of resistance and related concepts surrounding electricity, such as Ohm’s Law. Here’s what you need to know to get started!
Definition & laws of resistance
Resistance is a measure of opposition to current flow. This opposition occurs due to the repeated collisions between charge carriers in the tested material against each other. Did you know that resistance of the material also varies based on the cross sectional area and length? The smaller the cross sectional area and the longer the material, the higher the resistance will be!
Ohm’s Law states that the potential difference (voltage) across a metallic conductor is directly proportional to the current that is passing through it, provided that the physical conditions do not change. This is true in Ohmic materials, in which the resistance is constant. This law allows us to calculate related values when we know the potential difference (V), current (I) and resistance (R) of the material.
The SI unit for resistance is Ohm (Ω). 1 Ohm of resistance would allow 1 Volt of potential difference generate 1 Ampere of current. The following formula describes this relationship:
R = V / I
(R – resistance (Ω), V – potential difference across the component (V), I – current (A))
How to measure resistance of a material experimentally
What you need:
2. Power Source (e.g. Batteries)
Here are the steps to measure resistance and find out the resistance of a metallic conductor:
1. Connect the circuit diagram per the above picture where V is the Voltmeter, A is the Ammeter, Ω is the unknown Resistor.
2. Ensure that the current measuring Ammeter is in series with the Resistor material.
3. Connect the Voltmeter across the Resistor.
4. Measure the current reading from the Ammeter. This will be the ‘I’ value in the formula.
5. Measure potential difference that is across the resistor using the Voltmeter. This will be the ‘V’ value in the formula.
6. You can now calculate the Resistance of the material using the formula: R =V/I
Measuring effective resistance of resistors
There are two basic methods of connecting resistors or other devices together. Resistors can either be connected in parallel or series configuration. How can we find the effective resistance for resistors in series and parallel connections?
Resistors in series
For resistors arranged in series, there is only one pathway for the current to flow, and the current from one resistor flows into the next. The effective resistance (R) of three resistors R1, R2 and R3 are:
R = R1 + R2 + R3
If there are n resistors in the series, the effective resistance is calculated like so:
R = R1 + R2 + … + Rn
Exam tip! It is important to note that for effective resistance in a series connection, R must be larger than the largest of individual resistances.
What is the effective resistance of this circuit?
R = 6 Ω + 6 Ω = 12 Ω
Resistors in parallel
Resistors in a parallel circuits are arranged across each other, providing multiple pathways for current to flow. The effective resistance of R in resistors R1, R2, and R3 in parallel is as follows:
If there are n resistors in parallel, the effective resistance is calculated like so:
Exam tip! It is important to note that for connections in parallel, the effective resistance of R is always smaller than each individual resistance.
What is the effective resistance of this circuit?
R = 1/0.0117 = 85.6 Ω
Bonus: How can we measure resistance in a circuit that has both parallel and series connections?
We can find the total resistance by calculating the effective resistance of the resistors in parallel, and then adding that resistance value to the resistors in series for the total resistance.
Resistance of resistor in series: 6 Ω
Resistance of resistors in parallel:
R = 1/0.0167 = 6 Ω
Now that we have combined the resistance of the resistors in parallel, we can now calculate the total resistance of the circuit similar to how we would with a normal circuit diagram in series.
Total resistance of circuit: 6Ω + 6Ω = 12Ω
Resistivity of a wire
The resistivity of a wire is calculated using the following formula where R is the resistance, is the resistivity of the wire, L is the length of the wire, and A the cross-sectional area of the wire.
Temperature increase in metallic conductors
The I/V graph of a metallic conductor is charted by a straight line that passes through the X-axis and Y-axis. Resistance is independent of current as they obey Ohm’s law. In metal, resistance is known as the reduction of the speed of electrons because of the collision that occurs lattice ions.
Should the temperature of the metallic conductor remain constant, the size of the vibration in the lattice ions will remain the same. Thus, the resistance of the metallic conductor would also stay the same. Here is an example of the I/V graph for metallic conductor at constant temperature:
Temperature increase on filament lamp
On the I/V graph, when the current increases, the ratio V/I increases as well. Thus, when the temperature of the filament lamp increases, so does its resistance.
The potential difference in a filament lamp will increase alongside the current due to dissipating energy and heat increases, which results in higher temperature. Here is an example of the I/V graph for a filament lamp.
I/V graph for a semiconductor diode
A diode is a semiconductor that has high resistance and low resistance in opposite directions. Should potential difference be applied across the diode through the direction of low resistance, it will be forward biased. If potential difference is applied through the direction of high resistance, it will be in reverse bias.
Should the reverse bias potential difference be too high, the diode may break down, causing the current to be infinite and resulting in a short circuit. Here is the I/V graph for a semiconductor diode.
There is so much to cover about resistance for electric currents, and it can feel overwhelming if you are unsure. If you feel that way, you should enrol in a physics tuition class today! You’ll be able to clarify all the topics that you are unclear about and your tutor can help to guide you on the definitions, examples and applications of important physics concepts.
Sign up for a physics tuition class today and enhance your physics learning experience!