Question

Assertion: When a wire is stretched to two times its length keeping the diameter same, its resistance becomes 4 times.
Reason: Resistance is directly proportional to length of wire.
A) Both assertion and reason are correct and reason is the correct explanation for assertion.
B) Both assertion and reason are correct but reason is not the correct explanation for assertion.
C) Assertion is correct but reason is incorrect.
D) Assertion is incorrect but reason is correct.

Answer 1

Hint: Remember, resistance is directly proportional to length of the wire and is inversely proportional to area of cross-section. As the diameter is the same so, the cross-sectional area will not change.


Formula Used:
The formula of resistance is given by
$$R = \dfrac{{\rho l}}{A}$$
Where $R$ is the resistance, $\rho $ is the resistivity of the material, $l$ is the length and $A$ is the cross-sectional area.

Complete step by step answer:
RESISTANCE: It is defined as the measure of opposition acting on the flow of current. The resistance of an object depends upon two factors i.e. material of the object and shape of the length.
The formula used for calculating resistance is given as
$R = \dfrac{{\rho l}}{A}$
Where $R$ is resistance in an object, $\rho $ is the resistivity of the material, $l$ is the length of the object and $A$ is area of cross-section in ${m^2}$.
Resistivity of a material is defined as the resistance of the material per unit length, per unit cross-sectional area.
$\rho = R\dfrac{l}{A}$
Now, resistance of an object is directly to the length of material, therefore, resistance of object increases with the increase in length of object.
Therefore, when the length of the wire is doubled, resistance of the object is also doubled.
Therefore, option (D) is the correct answer.

Additional Information: As we all know, resistance of the object is given by
$R = \dfrac{{\rho l}}{A}$
Now, assuming $\rho $ as the constant of proportionality, we get
$ \Rightarrow R\alpha \dfrac{l}{A}$
Therefore, resistance is directly proportional to length of object and inversely proportional to cross-sectional area.

Note: There might also be a confusion in resistivity and resistance as both the words are similar. Remember, resistance and resistivity are different things. Resistance is the property which opposes the flow of current whereas resistivity is the resistance offered by the material per unit length and cross-section area.