Current measured by the ammeter (A) in the reported circuit when no current flows through 10 Ω resistance, will be ________________ A.

Solution

Physics sir · 4 steps

No current in the 10 Ω means a balanced bridge: find R, drop the middle wire, then use Ohm's law.

1. Balanced bridge. If no current flows through the 10 Ω resistor, its two ends are at the same potential. That is a balanced Wheatstone bridge, so the ratios on the two sides must match.

   R/4 = 3/6 ⇒ R = 2 Ω

2. Remove the middle. With no current in it, the 10 Ω resistor can be removed. The upper path is 2 + 4 = 6 Ω and the lower path is 3 + 6 = 9 Ω. These two paths are in parallel.
3. Equivalent resistance. R_(eq) = (6 × 9)/(6 + 9) = 54/15 = 3.6 Ω.
4. So. The ammeter carries the full current from the battery: I = 36/3.6 = 10 A.

The common slip: 2.4. Adding the two paths in series, 6 + 9 = 15 Ω, gives 36/15 = 2.4 A. The two paths are in parallel between the same two nodes.

The idea to keep. Zero current in the middle resistor of a bridge tells you it is balanced. Use the ratio condition to find the unknown, then treat the middle resistor as if it were not there.

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