Answer

Verified

347.7k+ views

**Hint:**Resistivity is a measurement of a material's resistance to electrical conduction at a given size. Although these terms are less often used, resistivity may often be referred to as specific electrical resistance or volume resistivity.

**Complete answer:**

As current flows sequentially through the resistors, they are assumed to be in sequence. The current through and resistor is the same so there is only one direction for the charges to pass through. The algebraic number of the individual resistances equals the corresponding resistance of a group of resistors in a sequence relation.

Each resistor receives the same amount of current from the voltage source, so the current through each resistor is the same. The voltage provided by the voltage source and the resistance of the resistors determine the current flowing through the circuit. If a current passes through each resistor, a potential reduction occurs that is equal to the loss of electric potential energy.

Electrical resistance of a conductor with a unit cross-sectional area and length is called resistivity. Resistivity is a property of each material that can be used to compare the ability of different materials to conduct electric currents. Weak conductors have a high resistivity.

We know that

\[{\text{R}} = \dfrac{{\rho L}}{A}\]

When the lengths of 'n' conducting wires are the same

but having resistivities 1,2,3…n are connected in series.

\[{\text{R}} = {{\text{R}}_1} + {{\text{R}}_2} + \ldots \ldots \ldots {{\text{R}}_n}\]

\[ \Rightarrow \dfrac{{\rho L}}{A} = \dfrac{L}{A}(1 + 2 + 3 + \ldots ..n)\]

\[ \Rightarrow \dfrac{{\rho L}}{A} = \dfrac{L}{A} \times \dfrac{{n(n + 1)}}{2}\]

Hence, equivalent resistivity \[\rho = \dfrac{{n(n + 1)}}{2}\]

**Note:**Conductivity is the reciprocal of resistivity, and it, like resistivity, characterises materials by how well electric current passes through them. mho per metre, or ampere per volt-metre, is the metre-kilogram-second unit of conductivity. High conductivities and low resistivities are characteristics of good electrical conductors. High resistivities and low conductivities are characteristics of good insulators, or dielectrics.

Recently Updated Pages

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Which are the Top 10 Largest Countries of the World?

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Difference Between Plant Cell and Animal Cell

The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths

Change the following sentences into negative and interrogative class 10 english CBSE

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Select the word that is correctly spelled a Twelveth class 10 english CBSE