Dependence of Potential Difference Across a Resistor on Current with Graph

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What is Ohm's Law?

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 (Frequently Asked Questions)

Question 1: What factors affect the resistance of a Wire?

Answer: Resistance of a wire depends upon certain factors. Different wires have different resistances. Factors affecting the resistance of a wire are as follows.

  1. Material- The type of material of which the wire is made. This has to do with the conductivity of certain elements. Some materials offer more resistance because they are less conductive. For example, iron is more conductive than copper.

  2. Length- greater the length of the resistor, more is the resistance offered.

  3. The thickness of the wire- wires with larger diameter offer less resistance.

  4. Temperature- If the temperature of the conductor increases, so does the resistance offered.

Question 2: What are the limitations of Ohm's Law?

Answer: The limitations of Ohm’s law are as follows.

  • Ohm’s law does not work in unilateral circuits. These are circuits or networks where the flow of current is unidirectional. For example, diodes, transistors, etc.

  • It is not applicable to non-linear elements. There are certain electrical elements that offer different resistance to different values of current and voltage. It means that these elements do not offer current directly proportional to the potential difference applied.

  • The relation between potential differences is sign dependent, which means that if a negative potential difference is applied across the ends of the conductor, it won’t give the same amount of current as that of the positive potential difference of the same magnitude.

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