For maximum power transfer, how must the load resistance compare to the source resistance?

• A. Load resistance must be zero
• B. Load resistance must be greater than the source resistance
• C. Load resistance must equal the source resistance
• D. Load resistance must be double the source resistance

Answer: (C)

Maximum power transfer occurs when the load resistance equals the source's internal resistance. Model the source as an ideal voltage source Vth in series with Rs. The power delivered to the load is P = Vth^2 · RL / (RL + Rs)^2. This expression is maximized when RL = Rs. At that point, half the voltage drops across the internal resistance and half across the load, giving I = Vth / (2Rs) and Pmax = Vth^2 / (4Rs). If the load is too small, too much power is wasted in Rs; if the load is too large, little current flows and the load power drops.