The ratio of heat dissipated per second through the resistance 5 Ω and 10 Ω in the circuit given below is:

Solution

Physics sir · 3 steps

The 5 Ω and 10 Ω share the same two junctions, so use P = V²/R and the 20 Ω does not matter.

1. Same voltage. The 5 Ω and 10 Ω resistors connect between the same two points, so they are in parallel and have the same voltage V across them. With V common, the right formula for heat per second is P = V²/R.

   P₅/P₁₀ = (V²/5)/(V²/10) = 10/5 = 2

2. Check with numbers. The parallel pair gives 10/3 Ω, so the total is 70/3 Ω and the current is 3/7 A. The pair then has 10/7 V across it, which gives P₅ = 20/49 W and P₁₀ = 10/49 W.
3. So. The heat dissipated per second is in the ratio 2 : 1, which is option (b).

The idea to keep. For parallel resistors the voltage is common, so P ∝ 1/R and the smaller resistor heats more. For series resistors the current is common, so P ∝ R.

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