Question

if the two wires carries current in the ratio 3:4, for the same time t, then the heat produced is equal. then find the ratio of respective resistance of the wires?​

Answer 1

Answer:

Ratio of specific resistance = 16 : 9

Explanation:

We know that,

Heat produced = I²Rt

H = I²Rt

Hence,

Heat produced by first wire = H₁

Heat produced by second wire = H₂

Therefore,

H₁ / H₂ = (I₁² R₁ t) / (I₂² R₂ t)

H₁ / H₂ = (I₁ / I₂)² * (R₁ / R₂)

Given that,

H₁ = H₂

I₁ / I₂ = 3 / 4

Putting these values in we get,

1/1 = (3/4)² * (R₁ / R₂)

R₁ / R₂ = 16 / 9

We know that,

Resistance = Specific resistance * Length/Area

ie,

Resistance ∝ Specific resistance

R ∝ ρ

Hence,

R₁ / R₂ = ρ₁ / ρ₂

ρ₁ / ρ₂ = 16 / 9