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The electrical resistance of a uniform conductor is given in terms of resistivity by:

R=

a

ρl

where l is the length of the conductor in SI units of meters,

a is the cross-sectional area (for a round wire a=πr

2

if r is radius) in units of meters squared, and ρ is the resistivity in units of ohm·meters.

∴R

A

=

πr

2

ρl

and R

B

=

πr

2

2lρ

Resistance in parallel will be

R

eq

1

=

R

A

1

+

R

B

1

=

ρl

πr

2

+

2lρ

πr

2

=

ρ2l

3πr

2

∴R

eq

=

3πr

2

2ρl

Now the ratio between total resistance and reistance of wire A is

R

A

R

eq

=

πr

2

ρl

3πr

2

2ρl

=

3

2

389

Duhn

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