Question

Find x if
$\bf \: x - \frac{1}{2} = 2$

​

Answer 1

Answer:

A wire of length = l and resistance = R , if it streched such that its length becomes 3 times more of its initial one. Find the ratio of initial resistance to the newly obtained resistance.

To Find:-

Find the ratio.

Solution:-

Case 1:-

\sf\dashrightarrow \: R = \dfrac { ρl } { A_1 } ⇢R=

A

1

ρl

\sf\dashrightarrow \: R = \dfrac { ρl } { 3A_2 } ⇢R=

3A

2

ρl

. . . . ( 1 )

Case 2:-

\sf\dashrightarrow \: R' = \dfrac { ρ \times 3l } { A_2 } ⇢R

′

=

A

2

ρ×3l

\sf\dashrightarrow \: R' = \dfrac { 3ρl } { A_2 } ⇢R

′

=

A

2

3ρl

. . . . ( 2 )

Now ,

We have do to divide ( 1 )/( 2 ) then we get:-

\sf\dashrightarrow \: \dfrac { R } { R' } = \dfrac { \: \: \dfrac { ρl } { 3A_2 } \: \: } { \dfrac { A_2 } { 3ρl } } ⇢

R

′

R

=

3ρl

A

2

3A

2

ρl

\sf\dashrightarrow \: \dfrac { R } { R' } = \dfrac { ρl } { 3A_2 } \times \dfrac { A_2 } { 3ρl } ⇢

R

′

R

=

3A

2

ρl

×

3ρl

A

2

\sf\dashrightarrow \: \dfrac { R } { R' } = \dfrac {1 } { 9 }⇢

R

′

R

=

9

1

\sf\dashrightarrow \: R : R' = 1 : 9 ⇢R:R

′

=1:9

Answer 2

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