Question

(a) On which factors does the resistance of conductor depend? Define resistivity and state its SI unit.
(b) Give the value of total resistance and total current flowing in the circuit.

Answer 1

The resistance of a material depends on several quantities like length of the conductor, cross-section area of the conductor and resistivity of material like as we know rubber is bad conductor and copper is a good conductor of electricity (resistivity .depends on the material type).
We also know that the total current of a circuit when divided in a branch then it is divided through an inverse ratio of resistance in corresponding branches.

Complete step by step solution:
(a):
Following are the factors on which the resistance of a conductor depends:
Length: Whenever we pass current through a wire, we sometimes observe that when the length of wire is large then current though it low. And from the formula $V = IR$ we know that current is inversely proportional to resistance thus we can say that resistance is directly proportional to length of the wire.
Nature of the material: As we discussed in the hint that the resistance of the material also depends on the nature of the material like glass, rubber, plastic are bad conductors while copper, iron and some other metals are very good conductors of electricity. This property of metal is called resistivity. Therefore, resistivity of the metal is directly proportional to the resistance of the material.
Area: Talking of the cross-section area of the conductor you might have noticed that thick wires are often used to carry heavy current loads. That means resistance is inversely proportional to the area of the cross section of the wire.
Temperature: Resistivity is indirectly proportional to the temperature. In other words, as you increase the temperature of materials, their resistivities will decrease.
Formula for resistance: $R = \dfrac{{\rho l}}{A}$
Resistivity; Resistivity is the resistance per unit length and cross-sectional area. It is the property of the material that opposes the flow of charge or the flow of electric current. The unit of resistivity is ohm meter ( $\Omega m$ ).

(b):
In the given circuit, the two $2\Omega$ resistors are in series with each other and these resistors are in parallel with other two $2\Omega$ resistors which are in series with each other.
${R_1} = 2 + 2 = 4\Omega$
${R_2} = 2 + 2 = 4\Omega$
Now these two resistances are in parallel therefore, resultant of these two can be given as:
$R = \dfrac{{{R_1}{R_2}}}{{{R_1} + {R_2}}}$
$R = \dfrac{{4 \times 4}}{{4 + 4}}$
$R = 2\Omega$ This is the total resistance of the circuit.
Now from $I = \dfrac{V}{R}$
$I = \dfrac{6}{2} = 3A$ This is the total current flowing through the circuit.

Note: There is a difference between resistance and resistivity which can be explained as Resistance of a conductor depends on length, thickness, nature of material and temperature of the conductor; while resistivity of a substance depends on the nature of the substance and temperature.