[Circuits] 2321 Problems

23211(a) Equivalent resistor: \(2 + 2 || (1+R_x)=\frac{8+4R_x}{3+R_x}\) Voltage across \(R_x\): \(4 \times \frac{(2+2R_x)/(3+R_x)}{(8+4R_x)/(3+R_x)} \times \frac{R_x}{1+R_x}=\frac{2R_x}{2+R_x}\) Power consumption of \(R_x\): \(\frac{4R_x}{(2+R_x)^2}=\frac{4}{4/R_x+4+R_x}\) \(\therefore\) Using AM-GM inequality, when \(R_x=2(\text{k}\Omega)\), power consumption maximized to \(0.5(\text{mW})\). 23..