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Q.) => Wires A and B are made from same material . Wire A has a lenght 12m and weight 50 g ,, while wire B is 18m long and weight 40 g . Then the ratio
( Ra / Rb ) of their Resistances will be .
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∵ wires are made of same material
∴ density and resistivity of both the wire are same .
Now, density of A = density of B
∵ density = Mass/Volume and volume = area × Length
∴ density of A = Mass of A/area of A × length of A
density of B = mass of B/area of B × length of B
Given, mass of A , Ma = 50g
length of A , La = 12 m
Mass of B , MB = 40g
length of B ,Lb = 18 m
Now, 50/Aa × 12 = 40/Ab × 18
Aa/Ab = 90/48 = 45/24
Hence, ratio of area of wire A and B = 45 : 24
Now, use formula,
R = ρL/A
R is directly proportional to length and inversely proportional to area.
so, Ra/Rb = La/Aa × Ab/Lb
= (La/Lb) × (Ab/Aa)
= 12/18 × 24/45
= 48/135
Hence, ratio of resistance Ra and Rb = 16 : 45
∴ density and resistivity of both the wire are same .
Now, density of A = density of B
∵ density = Mass/Volume and volume = area × Length
∴ density of A = Mass of A/area of A × length of A
density of B = mass of B/area of B × length of B
Given, mass of A , Ma = 50g
length of A , La = 12 m
Mass of B , MB = 40g
length of B ,Lb = 18 m
Now, 50/Aa × 12 = 40/Ab × 18
Aa/Ab = 90/48 = 45/24
Hence, ratio of area of wire A and B = 45 : 24
Now, use formula,
R = ρL/A
R is directly proportional to length and inversely proportional to area.
so, Ra/Rb = La/Aa × Ab/Lb
= (La/Lb) × (Ab/Aa)
= 12/18 × 24/45
= 48/135
Hence, ratio of resistance Ra and Rb = 16 : 45
abhi178:
I think answer should be 16 : 45.
Ra / Rb = La / Lb × ( Rb / Ra )^2
yeah ,, i also think that answer is 16 : 45
Sir , Ratio of Area is wrong i think
what will he ratio then ?
Tell me where wrong , I will correct then
Not sure but = Mass will be = πr^2×d for both Ma and Mb ,as we need to take out ratio of their Radius . Ma / Mb = ( ra / rb )^2 × La / Lb after putting values and solving (ra / rb)^2 is coming 15 / 8
:) not require to find radii. Just take area ratio and Length ratio . And got the answer.
☺.
nice answer
Answered by
1
ANSWER:-
R = ρ L/LA
And, volume, V=AL
⟹R=ρ L²/v
And,
mass m=σV where σ= density of material
⟹R = ρσ L²/m
Hence,
Ra/Rb = (La/Lb)²mb/ma
⟹Ra/Rb = (12/18)² 40/50
⟹Ra/Rb = 16/45
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