Two wires of same material and same length have radii r1 and r2. compare their resistances.
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Resistance for 1st body be R₁ & of second body be R₂
we know,
R = ρ ( L / A )
Since given object is a wire, its diameter becomes Area of cross section ( A ).
I.e ,
for 1st wire A = 2r₁ & for 2nd wire A = 2r₂
∴ R₁ = ρ ( L₁ / 2r₁ )
&
R₂ = ρ ( L₂ / 2r₂ )
Since their lengths are same,
L₁ = L₂ =L
∴ R₁ = ρ ( L / 2r₁ )
&
R₂ = ρ ( L / 2r₂ )
R₁/R₂ = [ ρ ( L / 2r₁ ) ] ÷ [ ρ ( L / 2r₂ ) ]
= 2r₂ / 2r₁
= r₂ / r₁ //
we know,
R = ρ ( L / A )
Since given object is a wire, its diameter becomes Area of cross section ( A ).
I.e ,
for 1st wire A = 2r₁ & for 2nd wire A = 2r₂
∴ R₁ = ρ ( L₁ / 2r₁ )
&
R₂ = ρ ( L₂ / 2r₂ )
Since their lengths are same,
L₁ = L₂ =L
∴ R₁ = ρ ( L / 2r₁ )
&
R₂ = ρ ( L / 2r₂ )
R₁/R₂ = [ ρ ( L / 2r₁ ) ] ÷ [ ρ ( L / 2r₂ ) ]
= 2r₂ / 2r₁
= r₂ / r₁ //
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