Question

Two conducting wires of the same material and of the equal length and equal diameters are first connecting in series and then parallel in an electric circuit. The ratio of heat produced in series and parallel combination whould be

Answer 1

ρ₁ = ρ₂ (same material)

l₁ = l₂

A₁ = A₂ (same diameter)

R₁ = ρ₁ x l₁ / A₁

R₂ = ρ₂ X l₂ / A₂

When connected in series,

Equivalent resistance (Rs) = R₁ + R₂ = 2R₁ ( R₁ = R₂)

H₁ = I₁² X Rs X t = I₁² X 2R₁ X t

When connected in parallel,

Equivalent resistance (Rp) = R₁ X R₂ / R₁ + R₂ = R₁/2 ( R₁ = R₂)

H₂ = I₂² X Rp X t = I₂² X R₁/2 X t

Ratio = H₁ : H₂ = I₁² X 2R₁ X t : I₂² X R₁/2 X t = 4 : 1 ( I₁ = I₂)