Question

Two electric heaters have power ratings P₁ and P₂, at voltage V. They are connected in series to a dc source of voltage V. Find the power consumed by the combination. Will they consume the same power if connected in parallel across the same source?

Answer 1

When the heaters are connected in series:

The resistance of these heaters are

`R_1 = V^2/P_1` and `R_2 = V^2/P_2`

Here, R = R₁ + R₂

It P is the effective power of the combination,

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

⇒ `1/P = 1/P_1 + 1/P_2`

When the heaters are connected in parallel:

Again, the resistances of these heaters are

`R_1 = V^2/P_1` and `R_2 = V^2/P_2`

Here, `1/R = 1/R_1 + 1/R_2`

Multiplying both sides by V²,

`V^2/R = V^2/R_1 + V^2/R_2`

⇒ P = P₁ + P₂

Connecting them in series or parallel over the same source will result in varying power consumption.