Power dissipation formula for external resistor

Steps:

• Current I = E / (R + r).
• Power P = I² R = E² R / (R + r)².
• Rearrange: E² = P (R + r)² / R.
• Maximum E = (R + r) √(P / R).

Why D is correct:

• Matches the solved formula E = \frac{R \sqrt{P}}{R + r} from rearranging P = \frac{E^2 R}{(R + r)^2} under maximum safe power condition.

Why the others are wrong:

• A assumes R > r for defined value but ignores correct total resistance.
• B derives from total circuit power, not load power.
• C uses R - r, invalid for series circuit.

Final answer: D