Question

1. State whether the following statement is correct. “If the current through the cell is from its positive to negative, against the direction of emf, then the potential drop across the internal resistance aids the emf of the cell.

2. You are given two cells. Group them so that they give more voltage. Arrive at the expression for effective emf and internal resistance.

Answer 1

1. True. Internal resistance and lost volt always opposes current ow through the cell”.

2. 

Consider two cells in series. Let ε₁ , r₁ be the emf and internal resistance of first cell. Similarly ε₂ , r₂ be the emf and internal resistance of second cell. Let I be the current in this circuit.

From the figure, the P.d between A and B

V_A – V_B = ε₁ – 1 ………(1)

Similarly P.d between B and C

V_B – V_C = ε₂ – 1 ……..(2)

Hence, P.d between the terminals A and C

V_AC = V_A – V_C = V_A – V_B + V_B – V_C

V_AC = [V_A – V_B] + [V_B – V_C]

when we substitute eqn. (1) and (2) in the above equation.

V_AC = ε₁ – Ir₁ + ε₂ – Ir₂

V_AC = (ε₁ – ε₂) – I(r₁ + r₂)

V_AC = ε_eq – Ir_eq

where ε_eq = ε₁ + ε₂, and r_eq = r₁ + r₂