Terminal potential difference in a cell with internal resistance

Steps:

• The emf E is the total voltage supplied by the cell.
• Current I passes through internal resistance r, producing a voltage drop of Ir.
• The voltage across external resistor R is IR.
• By Kirchhoff's voltage law, E = Ir + IR, so E - Ir = IR.

Why A is correct:

• A states E - Ir, the terminal potential difference across R, matching the rearranged form of the circuit equation from Kirchhoff's law.

Why the others are wrong:

• B: Subtracts IR (external drop) instead of Ir (internal drop), inverting the voltage balance.
• C: Adds Ir to E, which contradicts the opposing nature of the internal drop.
• D: Sets E = IR, neglecting internal resistance r entirely.

Final answer: A