For a load connected to a Thevenin source, which statement is correct about maximum power transfer?

For a load connected to a Thevenin source, which statement is correct about maximum power transfer?

• A. P_max occurs when R_L = 0
• B. P_max occurs when R_L = ∞
• C. P_max occurs when R_L = R_th
• D. P_max is independent of R_L

Answer: (C)

The power delivered to a load from a Thevenin source is maximized when the load resistance matches the source’s internal (Thevenin) resistance. If you replace the source with its Thevenin equivalent, a voltage source V_th in series with R_th, the load power is P = V_th^2 · R_L / (R_th + R_L)^2. With V_th and R_th fixed, maximizing P means maximizing the function R_L / (R_th + R_L)^2 with respect to R_L. Take the derivative and set it to zero: it gives R_L = R_th. At this point, the maximum power is P_max = V_th^2 / (4 R_th). If the load is 0 (shorted) or infinite (open), the load power is zero, so those cases are not maximum.

The power delivered to a load from a Thevenin source is maximized when the load resistance matches the source’s internal (Thevenin) resistance. If you replace the source with its Thevenin equivalent, a voltage source V_th in series with R_th, the load power is P = V_th^2 · R_L / (R_th + R_L)^2. With V_th and R_th fixed, maximizing P means maximizing the function R_L / (R_th + R_L)^2 with respect to R_L. Take the derivative and set it to zero: it gives R_L = R_th. At this point, the maximum power is P_max = V_th^2 / (4 R_th). If the load is 0 (shorted) or infinite (open), the load power is zero, so those cases are not maximum.