Physics, asked by shanku91, 1 month ago

find the ratio of resistances of copper rods X and Y of length 30 cm and 10cm respectively and having radii 2cm and 1 centimetre respectively​

Answers

Answered by sijit1981
1

Answer:

Radius of first wire = 2 cm

So,

Area of cross section of first wire =

\pi( {r}^{2} ) = \pi( {2}^{2} ) = 4\pi \: cm ^{2} π(r

2

)=π(2

2

)=4πcm

2

Radius of second wire = 1 cm

So,

Area of cross section of second wire=

\pi( {r}^{2} ) = \pi( {1}^{2} ) = \pi \: cm ^{2} π(r

2

)=π(1

2

)=πcm

2

General formula of resistance R =

\rho \: \frac{length}{area} ρ

area

length

Resistivity of both wires is same because both wires are made of same copper material.

So, Resistance of first wire =

r _1 = \rho \: (\frac{30}{4\pi} ) \: ohmr

1

=ρ(

30

)ohm

and Resistance of second wire =

r _2 = \rho \: (\frac{10}{\pi} ) \: ohmr

2

=ρ(

π

10

)ohm

So, the ratio of both resistance =

\frac{r_1 }{r _2} = \frac{\rho \: (\frac{30}{4\pi} ) }{ (\rho \frac{10}{\pi}) } = \frac{30}{40} = \frac{3}{4}

r

2

r

1

=

π

10

)

ρ(

30

)

=

40

30

=

4

3

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