Answer
Verified
376.5k+ views
Hint: Remember that the ratio of the resistances of two conductors will always be directly proportional to the ration of their lengths and it is inversely proportional to the ratio of their cross sectional areas.
Complete step by step answer:
The resistance of a short wire is lesser than the resistance of a long wire because in a long wire the electrons will collide with more ions as they pass through the wire. This makes the relationship between wire length and resistance proportional.
The area of cross section of wire is given by: $A = \pi {r^2}$
The resistance of wire is given by: $R = \dfrac{{\rho l}}{A}$
So, Area of cross section of first wire: ${A_1} = \pi {r_1}^2$
Area of cross section of second wire: ${A_2} = \pi {r_2}^2$
The ratio of areas of two wires will be:
$\dfrac{{{A_1}}}{{{A_2}}} = {\left( {\dfrac{{{r_1}}}{{{r_2}}}} \right)^2} = \dfrac{1}{4}$
Resistance of first wire: ${R_1} = \dfrac{{{\rho _1}{l_1}}}{{{A_1}}}$
Resistance of second wire: ${R_2} = \dfrac{{{\rho _2}{l_2}}}{{{A_2}}}$
The ratio of resistances of two wires will be:
$\dfrac{{{R_1}}}{{{R_2}}} = \dfrac{2}{3} \times \dfrac{3}{4} \times \dfrac{1}{{\dfrac{1}{4}}}$
$\therefore \dfrac{{{R_1}}}{{{R_2}}} = \dfrac{2}{1}$
Therefore, option D is the correct answer.
Note: The resistance of a thin wire will be greater than the resistance of a thick wire because thin wire has lesser electrons to carry current. This makes the relationship between resistance and the area of the cross section of a wire inversely proportional. The resistance that is offered per unit length and unit cross sectional area of that material when a known quantity of voltage is applied at its end is called specific resistance.
Complete step by step answer:
The resistance of a short wire is lesser than the resistance of a long wire because in a long wire the electrons will collide with more ions as they pass through the wire. This makes the relationship between wire length and resistance proportional.
The area of cross section of wire is given by: $A = \pi {r^2}$
The resistance of wire is given by: $R = \dfrac{{\rho l}}{A}$
So, Area of cross section of first wire: ${A_1} = \pi {r_1}^2$
Area of cross section of second wire: ${A_2} = \pi {r_2}^2$
The ratio of areas of two wires will be:
$\dfrac{{{A_1}}}{{{A_2}}} = {\left( {\dfrac{{{r_1}}}{{{r_2}}}} \right)^2} = \dfrac{1}{4}$
Resistance of first wire: ${R_1} = \dfrac{{{\rho _1}{l_1}}}{{{A_1}}}$
Resistance of second wire: ${R_2} = \dfrac{{{\rho _2}{l_2}}}{{{A_2}}}$
The ratio of resistances of two wires will be:
$\dfrac{{{R_1}}}{{{R_2}}} = \dfrac{2}{3} \times \dfrac{3}{4} \times \dfrac{1}{{\dfrac{1}{4}}}$
$\therefore \dfrac{{{R_1}}}{{{R_2}}} = \dfrac{2}{1}$
Therefore, option D is the correct answer.
Note: The resistance of a thin wire will be greater than the resistance of a thick wire because thin wire has lesser electrons to carry current. This makes the relationship between resistance and the area of the cross section of a wire inversely proportional. The resistance that is offered per unit length and unit cross sectional area of that material when a known quantity of voltage is applied at its end is called specific resistance.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE