# Resistance of a Conductor

**Resistance**

The hindrance to the flow of electric charge is known as Resistance. The obstruction posed in the way of current carrying particles by fixed particles creates resistance in an electric circuit. Since the current carrying particles follow a zig-zag path instead of straight path, they have collisions with the fixed particles and thus resistance occurs. In an electric circuit, the potential difference across the two terminals encourages the flow of current while at the same time the resistance discourages the flow of current. The measurement of the electric current in an electric circuit therefore, depends on these two factors primarily i.e. Potential Difference across the ends of the conductor and Resistance of the conductor.

The resistance of an electric circuit can be measured numerically. The SI unit for measuring electric current is ‘Ohm’ represented by Greek letter omega (Ω). In an electric circuit, the potential difference across a circuit is divided by the electric current ‘I’ gives the quantitative value of the Resistance in the circuit. This relationship is determined by **Ohm’s law** which states that the current flowing through a conductor between two points is directly **proportional **to the **voltage **across the two points.

I is directly proportional to V,

Potential difference/ Current = Resistance

i.e V/I = R

i.e 1 ohm = 1 volt/1ampere

Or I=V/R where R is the proportionality constant i.e. Resistance.

Therefore, 1 ohm is the resistance of a conductor such that when a potential difference of 1 volt is applied to its ends, a current of 1 ampere flows through it.

On the basis of their electrical resistance, all the substances can be divided in to three groups:

*(i) **Good Conductors*: are those substances which have very low electrical resistance. It allows electricity to flow through it easily.eg. Silver metal, Copper and Aluminium etc. Electric wires are made up of copper and aluminium because they have very low electrical resistance.

*(ii) **Resistors*: are those substances which have comparatively high electrical resistance. Alloys like nichrome, manganin and constantan (eureka) have high resistance i.e why they are used in electrical devices. Therefore, a resistor reduces the current in a circuit.

*(iii) **Insulators*: are those substances which have infinitely high electrical resistance.It does not allow electricity to flow through it, e.g Rubber, wood etc. Electricians wear rubber handgloves while working with electricity because it is an insulator and protects them from electric shocks.

*Factors affecting the Resistance of a conductor*:

The resistance of a given piece of wire or conductor depends on four factors: the length of the wire, the cross-sectional area of the wire, the resistivity of the material composing the wire and the temperature of the conductor or wire. For a given material, the resistance is inversely proportional to the cross-sectional area; for example, a thick copper wire has lower resistance than an otherwise-identical thin copper wire. Also, for a given material, the resistance is proportional to the length; for example, a long copper wire has higher resistance than an otherwise-identical short copper wire. The reciprocal of the resistance, 1/*R,* is called the ** conductance **and is expressed in mho. The resistance (R) and Conductance (G) for a conductor of uniform cross section can be calculated as:-

where is the length of the conductor, *A* is the cross-sectional area of the conductor, σ (sigma) is the electrical conductivity and ρ (rho) is the ** electrical resistivity **of the material. Here, the resistivity and conductivity are proportionality constants. Resistivity and conductivity are reciprocals

**i.e.**

The substances which are good conductors of electricity have very low resistance whereas the insulators have high resistance. Temperature has a positive effect over resistance as the resistance increases with the increasing temperature while when some conductors are cooled to extremely low temperatures show zero resistance and they are known as **superconductors **as current continuously flows through these conductors.

**Difference between Resistance and Resistivity is:**

**Combination of Resistances**

Apart from potential difference, current in a circuit depends on resistance of the circuit. So, it is necessary to combine two or more resistances to get the required current in the electrical circuits. Thus, the resistances can be combined in two ways: in series and in parallel. If we want to increase the total resistance, then the individual resistances are connected in series, and if we want to decrease the resistance, then the individual resistances are connected in parallel.

When two or more resistances are connected end to end consecutively, they are said to be connected in series. And on the other hand, when two or more resistances are connected between the same two points, they are said to be connected in parallel.

*Resistances in Series: *The combined resistance of any number of resistances connected in series is equal to the sum of the individual resistances.

When a number of resistances connected in series are joined to the terminals of a battery, then each resistance has a different potential difference across its ends which depend on the value of resistance. Thus, when a number of resistances are connected in series, then the sum of the potential differences across all the resistance is equal to the voltage of the battery applied. Also, the same current flows through each resistance which is equal to the current flowing in the whole circuit.

*Resistances in Parallel*: The reciprocal of the combined resistance of a number of resistances connected in parallel is equal to the sum of the reciprocal of all the individual resistances.

1/R = 1/R_{1} + 1/R_{2} + 1/R_{3}…………_{ }

Thus, when a number of resistances are connected in parallel then their combined resistance is less than the smallest individual resistance. We also should keep in mind that when a number of resistances are connected in parallel, then the potential difference across each resistance is the same which is equal to the voltage of the battery applied. And the current flowing through all the individual parallel resistances, taken together, is equal to the current flowing in the circuit as a whole. Thus, when a number of resistances are connected in parallel, then the sum of the currents flowing through all the resistances is equal to the total current flowing in the circuit.

*Disadvantages of Series circuits for domestic Wiring *

The arrangement of lights and various other electrical appliances in series circuit is not used in domestic wiring because

(i) If one electrical appliance stops working due to some defect, then all other appliances also stop working.

(ii) All the electrical appliances have only one switch due to which they cannot be turned on or off separately.

(iii) The appliances do not get the same voltage (220V) as that of the power supply line because the voltage is shared by all the appliances.

(iv) In the series connection of electrical appliances, the overall resistance of the circuit increases too much due to which the current from power supply is low.

*Advantages of Parallel circuits in Domestic wiring *

The arrangement of lights and various other electrical appliances in parallel circuits is used in domestic wiring because

(i) If one electrical appliance stops working due to some defect, then all other appliances keep working normally.

(ii) Also, each electrical appliance has its own switch due to which it can be turned on or turned off independently, without affecting other appliances.

(iii) Each electrical appliance gets the same voltage (220V) as that of the power supply line. Due to this, all the appliances will work properly.

(iv) In the parallel connection of electrical appliances, the overall resistance of the household circuit is reduced due to which the current from the power supply is high. Every appliance can, therefore, draw the required amount of current.

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