The heat generated in 1 minute between points A and B in the given circuit, when a battery of 9 V with internal resistance of 1Ω is connected across these points is ____ J.

Solution

Physics sir · 4 steps

Check the bridge first: 1 is to 2 as 2 is to 4, so the middle 1 Ω carries no current and drops out.

1. Balanced bridge. The upper path has 1 Ω then 2 Ω, and the lower path has 2 Ω then 4 Ω. Since 1/2 = 2/4, the two middle junctions are at the same potential. So no current flows through the vertical 1 Ω resistor.
2. Equivalent resistance. Remove the middle resistor. The upper path is 1 + 2 = 3 Ω and the lower path is 2 + 4 = 6 Ω. In parallel they give R_(AB) = (3 × 6)/(3 + 6) = 2 Ω.
3. Current from battery. The internal resistance is in series with R_(AB), so I = 9/(2 + 1) = 3 A.

   H = I² R_(AB) t = 3² × 2 × 60 = 1080 J

4. So. Only the external part between A and B counts, so the heat generated in 1 minute is 1080 J.

The common slip: 2430. Ignoring the internal resistance and using V²/Rt = 81/2 × 60 gives 2430, not 1080. The voltage across A and B is only 6 V.

The idea to keep. Before solving any bridge, compare the resistance ratios on both sides. If they match, delete the middle arm. Use internal resistance to find the current, but count heat only where asked.

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