Problem 14.81

จาก \(\wp = I^{2}R\)

\(\wp = (\frac{ε}{R + r})^{2}R\)

\(\wp = (\frac{4}{R + 1})^{2}R\)

\(\wp =\frac{16R}{(R + 1)^{2}}\)

\(\wp =\frac{16R}{R^{2} + 2R + 1}\)

\(\wp =\frac{16R}{R^{2} - 2R + 1 + 4R}\)

\(\wp =\frac{16R}{(R - 1)^{2} + 4R}\)

\(\wp =\frac{16}{4 +\frac{(R - 1)^{2}}{R}}\)

∴ ℘ จะมากที่สุด เมื่อ \(\frac{(R - 1)^{2}}{R}= 0\)

\(R - 1 = 0\)

\(R = 1 Ω \;\blacksquare\)