Two coils require 20 minutes and 60 minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be ___________ min.

Solution

Physics sir · 3 steps

Same source means same voltage, so in parallel the heating powers add, and 1/t adds the same way.

1. Heat at fixed voltage. With the same source voltage V, heat produced is H = V²/Rt. For the same H, the time needed is proportional to R, so R₁ ∝ 20 and R₂ ∝ 60.
2. Parallel combination. In parallel each coil still gets the full voltage V, so the total power is P₁ + P₂. Since P = H/t for the same H, the times combine like parallel resistances.

   1/t = 1/t₁ + 1/t₂ = 1/20 + 1/60 = (3 + 1)/60 = 1/15

3. So. The parallel combination produces the same heat in 15 minutes.

The common slip: 80. Adding the times directly, as you would for coils in series, gives 20 + 60 = 80 min, not 15.

The idea to keep. At constant voltage, the time to produce a fixed heat goes as R. Parallel: 1/t = 1/t₁ + 1/t₂. Series: t = t₁ + t₂.

Answer from the NTA final answer key. Solution by PrepWiser.