Question

Two heaters rated as (P₁, V) and (P₂, V) are connected in series across a dc source of `V/2` volt. The power consumed by the combination will be ______.

Options

• P₁ + P₂

• `(P_1 + P_2)/2`

• `(P_1P_2)/(2(P_1 + P_2))`

• `(P_1P_2)/(4(P_1 + P_2))`

Answer 1

Two heaters rated as (P₁, V) and (P₂, V) are connected in series across a dc source of `V/2` volt. The power consumed by the combination will be `bbunderline((P_1P_2)/(4(P_1 + P_2)))`.

Explanation:

Heater rating (P, V) gives resistance:

R = `V^2/P`

Resistance of heaters:

R₁ = `V^2/P_1`

R₂ = `V^2/P_2`

Series combination:

R_eq = R₁ + R₂

= `V^2/P_1 + V^2/P_2`

= `V^2((P_1 + P_2)/(P_1 P_2))`

Applied voltage (V') = `V/2`

Power consumed (P) = `V^(r2)/R_"eq"`

= `((V//2)^2)/(V^2((P_1 + P_2)/(P_1 P_2)))`

= `(V^2//4)/(V^2((P_1 + P_2)/(P_1 P_2)))`

= `(P_1 P_2)/(4(P_1 + P_2))`