Grade 12Mechanics
1. Length of a conductor is increased by 1% .Calculate the percentage change in its resistance at constant volume
1 Answer
Arun
Given:
Let the initial length of wire=l1
Final length of wire after stretching=l1+(1/100)l1
=l1(1+1/100)
=( 101/100 )l1
= 101/100 l1
Area of initial wire=A1
Area of final wire = A2
Volume of wire remains constant.
l1A1=l2A2
A2=l1A1/l2
As we know that
R = ρ l/A
R1/ R2 =( l1/A1 )/(l2/A2)
= l1A2/l2A1
= l1 (l1A1/l2)/l2A1
R1/R2 = l1^2/l2^2=101²/100²
R2=R1x101²/100²
(ΔR/R)×100=(R2-R1/R)×100=1.02%
The percentage increase in resistance IS 1.02%
Let the initial length of wire=l1
Final length of wire after stretching=l1+(1/100)l1
=l1(1+1/100)
=( 101/100 )l1
= 101/100 l1
Area of initial wire=A1
Area of final wire = A2
Volume of wire remains constant.
l1A1=l2A2
A2=l1A1/l2
As we know that
R = ρ l/A
R1/ R2 =( l1/A1 )/(l2/A2)
= l1A2/l2A1
= l1 (l1A1/l2)/l2A1
R1/R2 = l1^2/l2^2=101²/100²
R2=R1x101²/100²
(ΔR/R)×100=(R2-R1/R)×100=1.02%
The percentage increase in resistance IS 1.02%
Other Related Questions on mechanics
Three identical balls are placed on a frictionless
horizontal surface touching each other. They stick to
each other because of adhesive. Another ball of same
radius and mass m is placed over the void created by
the three balls. Find the forces applied by the balls
kept on the floor to each other if the system remains
in equilibrium.
Three identical balls are placed on a frictionless
horizontal surface touching each other. They stick to
each other because of adhesive. Another ball of same
radius and mass m is placed over the void created by
the three balls. Find the forces applied by the balls
kept on the floor to each other if the system remains
in equilibrium.
mechanics
Last Activity: 9 Months ago
A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.
11
21
31
41
A car loaded with water having total mass 1000 kg moves on a straight horizontal Road starting from rest under the action of a force of 100 Newton. The water spills throw a small hole in the bottom at a rate of 0.1 KG per second the velocity of cart after 300 seconds is nearly.
11
21
31
41
mechanics
Last Activity: 10 Months ago
A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mmat the free end, where a small mass of 2 g is positioned. determine(i) The velocity of the end when passing through the zero position(ii) The acceleration at maximum displacement(iii) The maximum kinetic energy of the mass
A metal strip clamped at one end vibrates with a frequency of 20 Hz and amplitude of 5 mm
at the free end, where a small mass of 2 g is positioned. determine
(i) The velocity of the end when passing through the zero position
(ii) The acceleration at maximum displacement
(iii) The maximum kinetic energy of the mass
mechanics
Last Activity: 3 Years ago
If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0
If a=x² find the displacement at t =3sec if body velocity at t= 0 sec is 0
mechanics
Last Activity: 3 Years ago