Terminal potential difference increases as variable resistance rises

Steps:

• Total circuit resistance = fixed resistor + R + internal r; increases with R.
• Current I = E / total resistance; decreases as R increases.
• Terminal potential difference V = E - I r; as I decreases, voltage drop I r decreases.
• Thus V increases with R, approaching emf E asymptotically.

Why D is correct:

• By definition, terminal pd V = E (R_ext / (R_ext + r)), where R_ext = fixed + R; rises with increasing R_ext per Ohm's law.

Why the others are wrong:

• A: Current I follows I = E / (R_ext + r); decreases hyperbolically with R.
• B: Electromotive force E is constant, independent of R.
• C: Potential difference across cell typically means full emf E; constant, not varying with R.

Final answer: D