Two cells are connected in opposition as shown. Cell E₁ is of 8 V emf and 2 Ω internal resistance; the cell E₂ is of 2 V emf and 4 Ω internal resistance. The terminal potential difference of cell E₂ is __________ V.

Solution

Physics sir · 4 steps

The stronger cell charges E₂, so its terminal voltage is E₂ + Ir, not E₂ - Ir.

1. Find the current. The cells oppose each other, so the net emf is 8 - 2 = 6 V. The only resistances are the two internal ones, 2 + 4 = 6 Ω. So I = 6/6 = 1 A.
2. Direction through E2. E₁ is stronger, so it sets the direction of the current. That current enters E₂ at its positive terminal, which means E₂ is being charged.

   V₂ = E₂ + I r₂ = 2 + (1)(4) = 6 V

3. Cross-check. E₁ is discharging, so its terminal voltage is 8 - (1)(2) = 6 V. The two cells sit across the same two points, so the two values must match, and they do.
4. So. The terminal potential difference of E₂ is 6 V.

The common slip: -2. Using V = E - Ir for E₂ gives 2 - 4 = -2, but E₂ is being charged, so Ir must be added.

The idea to keep. Use V = E - Ir for a cell that is discharging and V = E + Ir for a cell that is being charged. Check which way the current enters the cell before you choose the sign.

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