Understanding Ohm’s Law Through Real-World Resistor Graphs
Georg Simon Ohm, a German physicist, in the year 1827 deduced Ohm’s law which states that the current through a conductor is directly proportional to the potential difference applied across its 2 end-points. Mathematically, Ohm’s law is,
I ~ V
Where,
I = current b/w the 2 ends of the conductor
V = Potential difference applied across the conductor
Therefore,
I = V/R
Where R is the resistance offered by the resistor. Also written as,
V/I = R
The S.I. unit for Potential difference is Volts (V).
The S.I. unit for Current is Ampere (A).
The S.I. unit for resistance is Ohm, named after the scientist Georg Ohm who discovered it.
Ohm’s Law Explanation
A circuit is formed when a path is made for the charge to move through the conductor. This movement is caused due to the potential difference applied across the two end-points of the conductor. Current flows in the direction opposite to that of the flow of charge.
Potential difference refers to the amount of energy available for the current to move across the conductor. The potential difference across the two endpoints of the conductor is essential for the current to flow through the conductor. When current passes through the conductor, it gets some amount of friction or opposition from the conductor. This opposing force is called resistance. Resistance is very important, and many electrical devices operate based upon this concept of resistance and resistors—for example - electric heaters, steam iron, etc.
What is Ohm's Law formula?
The formula for Ohm’s Law is,
V/I = R
Where,
V = Potential difference applied across the 2 endpoints of the conductor
I = Current flowing between the 2 endpoints of the conductor
R = Resistance offered by the resistor
The resistance offered by the conductor depends upon certain factors. At a given temperature,
R ~ length of the wire
R ~ 1/cross sectional area
Mathematically,
R = pl/A
Where,
R = Resistance offered
p = Specific resistance or resistivity
l = Length of the wire
A = Cross-sectional area
Sometimes more than one resistor is applied in a circuit. This can be applied both in parallel or series arrangement.
Series Arrangement
Resistors are said to be placed in series if they are placed sequentially. Current flows through each of them one by one and current remains the same throughout the circuit. The total resistance of the circuit is obtained by adding the resistances.
R = R1 + R2 + ..... + Rn
Parallel Arrangement
Resistors are said to be placed in parallel if the circuit is branched into separate paths in between. One end of all the resistors is attached to the point from which the circuit branches out and the other end of all the resistors is attached to the point, at which all the branched paths meet again, in the circuit. The flow of current through each resistor is different and has to be calculated individually.
I = I1 + I2
R=( 1/R1 + 1/R2 + .....+ 1/Rn)
What Factors Affect Resistance?
Electric current is caused due to the free flow of electrons in a system. Every system or conductor offers some resistance to this flow of current. The resistance offered by a conductor is dependent on a variety of factors like the type of its material, length, cross-sectional area, and temperature of the conductor. Let us discuss each of these in detail.
Material of the Conductor
Some elements have more conductivity as compared to others. Elements that allow free flow of current through them are called electrical conductors. Metals are good conductors. For example - iron. Certain elements that do not allow this free flow are called insulators.
Length of the Wire
The length of the wire is directly proportional to the resistance offered by the wire. It is because the current has to travel all through the conductor, which will increase the resistance offered to its flow.
Cross-sectional Area of the Wire
The thickness of the wire used as a resistor also plays an important role. The thicker the wire, the more current can pass through it easily. The resistance offered is indirectly proportional to the cross-sectional area of the wire. A wire of thinner diameter will offer more resistance.
Temperature of the Conductor
When conductors are heated they offer more resistance because the kinetic energy increases which inhibits the smooth flow of current. The temperature of a conductor is thus directly proportional to the resistance offered.
Uses of Ohm’s Law
Ohm’s law is commonly used in most of the electronic devices around us like amplifiers, mobiles, laptops, electric heaters, and also in rockets and spaceships. Some more applications of Ohm’s law are as follows.
One of the most common examples of Ohm’s law in everyday life is the ceiling fan. The regulator of the fan, which regulates the speed of the fan uses Ohm’s law. The resistance is increased or decreased in the circuit by adjusting the regulator.
Fuse designs in our households show the application of Ohm’s law.
To calculate the power to be supplied to electric devices.
To calculate the resistance of any circuit.
FAQs on Potential Difference and Current Relationship in a Resistor: Graph Analysis
1. What is the fundamental relationship between the potential difference (V) across a resistor and the current (I) flowing through it, according to Ohm's Law?
According to Ohm's Law, the potential difference (V) across the ends of a given metallic wire in an electric circuit is directly proportional to the current (I) flowing through it, provided its temperature remains the same. This relationship is mathematically expressed as V ∝ I, or V = IR, where R is a constant called the resistance of the conductor.
2. How is the dependence of potential difference on current represented graphically?
The dependence of potential difference (V) on current (I) for an ohmic resistor is shown using a V-I graph. In this graph, potential difference (V) is typically plotted on the y-axis and current (I) on the x-axis. For a conductor that obeys Ohm's Law, this graph is a straight line passing through the origin. This linear shape visually confirms the direct proportionality between V and I.
3. How can you calculate the resistance of a conductor from its potential difference-current (V-I) graph?
The resistance (R) of a conductor can be calculated from the slope of its V-I graph. Since V = IR, the slope of the graph, which is the ratio of the change in V (on the y-axis) to the change in I (on the x-axis), gives the resistance. You can find the slope by picking any point on the line (apart from the origin) and dividing the corresponding potential difference value by the current value: R = V / I.
4. Why is it crucial to maintain a constant temperature while studying the relationship between V and I?
Maintaining a constant temperature is a critical condition for Ohm's Law. This is because the resistance of most conductors changes with temperature. If the temperature increases, the random motion of electrons and the vibrations of the ions in the conductor increase, leading to more frequent collisions and thus an increase in resistance. If the temperature were not constant, the V/I ratio would not be constant, and the V-I graph would not be a straight line, making the experiment invalid for verifying Ohm's Law.
5. What does the slope of a V-I graph signify, and how would it change for resistors with different resistance values?
The slope of a V-I graph (with V on the y-axis) directly represents the resistance (R) of the conductor.
- A steeper slope indicates a higher resistance, as a larger potential difference is required to produce the same amount of current.
- A gentler (less steep) slope indicates a lower resistance, as less potential difference is needed for the same current to flow.
6. What are the main limitations of Ohm's Law?
Ohm's Law is not a universal law and has several limitations. It is not applicable to:
- Non-ohmic conductors: Devices like diodes, transistors, and thermistors do not have a constant resistance. Their V-I graph is not a straight line.
- Unilateral networks: These are circuits that allow current to flow in only one direction, such as a diode. The relationship between V and I depends on the sign of the potential difference.
- Conductors at high temperatures: When a conductor like a filament bulb gets very hot, its resistance increases, and it ceases to obey Ohm's Law, resulting in a curved V-I graph.
7. How would the V-I graph for a resistor differ from that of a semiconductor diode?
The V-I graphs for a resistor and a semiconductor diode are fundamentally different, illustrating the difference between ohmic and non-ohmic devices.
- Resistor (Ohmic): The V-I graph is a straight line passing through the origin, indicating that resistance is constant and the current is directly proportional to the potential difference.
- Semiconductor Diode (Non-Ohmic): The V-I graph is a curved line. For a forward-biased diode, the current is negligible for low voltages and then increases exponentially after a certain threshold voltage (knee voltage). For a reverse-biased diode, the current is almost zero. This shows its resistance is not constant but changes with voltage.
