Question

A given resistance wire has A resistance of 6.0ohm . How will it's resistance change if a)only it's cross section area is doubled and b) only the radius of the wire is doubled.​

Answer 1

Answer:

Given :

R=6ohms

R=ρl/A-------------(1)

Wire is doubled so, Area =A=2A

length=l=l/2

New Reistance will be:

Rnew=ρ(l/2)/2A

Rnew=ρl/4A

Rnew=R/4-----(from equ 1)

Rnew=6/4=1.5 ohms

Hence new Reistance of wire is 1.5ohms.

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Answer 2

Given wire Resistance = 6 Ohms

Given wire Resistance = 6 OhmsSee the relation of Resistance to length and area

$R = p\frac{l}{A}$

When length doubles the Resistance also doubles . So it become 12 Ohms

When length doubles the Resistance also doubles . So it become 12 OhmsWhen area doubles the resistance becomes half and becomes 3 Ohms

When length doubles the Resistance also doubles . So it become 12 OhmsWhen area doubles the resistance becomes half and becomes 3 OhmsWhen Radius doubles the area becomes Pi *R^2 = 4 times Pi then original radius

When length doubles the Resistance also doubles . So it become 12 OhmsWhen area doubles the resistance becomes half and becomes 3 OhmsWhen Radius doubles the area becomes Pi *R^2 = 4 times Pi then original radiusTherefore, Resistance decreases by 4Pi times = 6/4Pi = 3/2Pi = 0.477 Ohms