Question

The resistance of a certain length of wire having diameter 5 mm is 10 ohm if the diameter is changed to 10mm the new resistance will become​

Answer 1

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Explanation:

GIVEN:

Diameter of wire [d1]=5mm

Resistance [R1]=10 ohm

Diameter of wire [d2]=100

Resistance of wire [R2]=?

R=ρl/A

A=πr²

l=2πr

R=ρ2πr/πr²

=2ρ/r

r1=5/2=2.5mm

r2=10/2=5mm

R1=10

R2=?

R2/R1=2ρ/r2*r1/2ρ

R2/R1=r1/r2

R2=R1*r1/r2

R2=10*2.5/5

R2=2*2.5

R2=5

Thus,the new resistance will be 5ohm

Answer 2

$Answer =>$

R' = 2.5ohms

$explanation =>$

Resistance of a resistor is given by

R = ρl/A

Where ρ - resistivity of the conductor

l - length of the resistor

A - cross-section Area of the conductor

A = πr^2

r - radius of the cross section area

Resistance is inversely proportional to the cross-section Area 'A'

If r = 2.5mm becomes r' = 5mm the new area becomes 4 times initial area

A' = 4A

R' = ρl/A' = ρl/4A = R/4 = 10ohms/4

R' = 2.5ohms