Question

A conductor of length L is connected to a dc Source of potential V. If the length of the

conductor is tripled, by stretching it keeping V constant,explain how do the following fac-

tors vary in the conductor:

(i) drift speed of electrons

(ii) resistance

(iii) resistivity​

Answer 1

i) drift speed of an electron:

$\large\rm { v_{d} \propto \frac {1}{1}}$

when the wire length is tripled, drift velocity gets one third

ii) resistance of conductor:

$\large\rm { R = \rho \frac{1}{a}}$

mass of the wire remains the same in both the conditions

mass before stretching = mass after stretching

$\large\rm { m_{1} = m_{2}}$

$\large\rm { v_{1} \rho_{1} = v_{2} \rho_{2}}$

$\large\rm { a_{1} l_{1} = a_{2} l_{2}}$

$\large\rm { a_{1} l = a_{2} (3l) \implies a_{2} = \frac {a_{1}}{3}}$

$\large\rm { R' = \rho \frac {l'}{a'} = 9 \frac { \rho l}{a} = 9R }$

new resistance is 9 times the original resistance.

Answer 2

Answer:

ANSWER

i)

drift speed of an electron

v

d

∝

l

1

when the wire length is tripled, drift velocity gets one third

ii)

resistance of conductor

R=ρ

a

l

mass of the wire remains the same in both the conditions

mass before stretching = mass after strecting

m

1

=m

2

v

1

ρ

1

=v

2

ρ

2

a

1

l

1

=a

2

l

2

a

1

l=a

2

(3l)⇒a

2

=

3

a

1

R

′

=ρ

a

′

l

′

=ρ

3

a

3l

=9

a

ρl

=9R

new resistance is 9 times the original resistance.