Question

An electrician has three spools of wire with him.The lengths of the wire are 42m 3cm,24m 26cm and 31m 15cm. what is the total length of the wire taken together ​

Answer 1

$\huge\boxed{Answer}$

Let the resistance of single copper wire be R

1

. If ρ is the specific resistance of copper wire, then

R

1

=

a

1

ρ×l

=

πr

1

2

ρ×l

- (i)

When the wire is replaced by six wires, let the resistance of each wire be R

2

. Then

R

2

=

A

2

ρ×l

=

πr

2

2

ρ×l

- (ii)

From equation (i) and (ii), we get

R

2

R

1

=

r

1

2

r

2

2

or

R

2

5

=

(9×10

−3

)

2

(3×10

3

)

2

;R

2

=45Ω

These six wires are in parallel. Hence the resistance of the combination would be R

2

=7.5Ω