For the network shown below, the value of V B - V A is ____________ V.

Solution

Physics sir · 4 steps

It is one closed loop: find the current first, then walk from A to B along either path.

1. One single loop. The battery, the 1 Ω and the 2 Ω resistors are all in series in one loop. The total resistance is 1 + 2 = 3 Ω, so I = 15/3 = 5 A.
2. Direction of current. The longer plate of the cell is its positive terminal, and it faces B. So the current flows from A through the cell and the 1 Ω to B, then back from B to A through the 2 Ω.

   V_A + 15 - (5)(1) = V_B ⇒ V_B - V_A = 10 V

3. Check the other path. Through the 2 Ω the current goes from B to A, so B is higher by IR = 5 × 2 = 10 V. Both paths agree.
4. So. V_B - V_A = 10 V.

The common slip: -10. Reading the cell backwards, with the long plate as negative, reverses the current and gives -10 instead of 10.

The idea to keep. To find a potential difference, walk from one point to the other: a cell from minus to plus adds its emf, and a resistor along the current subtracts IR. Any path gives the same answer.

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