Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

Solution

Physics sir · 3 steps

Same voltage, so use H = (V² t)/R: the smaller the total resistance, the more heat you get.

1. Pick the right formula. The voltage is fixed in both cases, so write heat as H = V²/Rt. With V and t the same, heat is inversely proportional to the total resistance.
2. Find both resistances. Let each filament have resistance R. In series, Rₛ = R + R = 2R. In parallel, Rₚ = (R × R)/(R + R) = R/2.

   Hₚ/Hₛ = Rₛ/Rₚ = 2R/(R/2) = 4

3. So. Heat in parallel to heat in series is 4 : 1, which is option (a).

The idea to keep. When the voltage is fixed, use P = V²/R, so heat goes as 1/R. When the current is fixed, use P = I²R, so heat goes as R.

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