Which statement best describes maximum power transfer for a Thevenin/Norton circuit?

Which statement best describes maximum power transfer for a Thevenin/Norton circuit?

• 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 occurs regardless of R_L

Answer: (C)

The idea is that to get the most power into the load from a Thevenin or Norton source, the load resistance should match the source’s internal resistance. In a Thevenin view, you have a voltage source Vth in series with Rth feeding the load RL. The power in the load is P = Vth^2 RL / (Rth + RL)^2. This expression reaches its maximum when RL equals Rth. At that point the current is I = Vth/(2Rth), the voltage across the load is Vth/2, and the load power becomes Pmax = Vth^2/(4Rth). If RL is either 0 (short) or infinite (open), the load power is zero, so those cases aren’t optimal. Therefore, matching the load to the source resistance delivers the greatest power.

The idea is that to get the most power into the load from a Thevenin or Norton source, the load resistance should match the source’s internal resistance. In a Thevenin view, you have a voltage source Vth in series with Rth feeding the load RL. The power in the load is P = Vth^2 RL / (Rth + RL)^2. This expression reaches its maximum when RL equals Rth. At that point the current is I = Vth/(2Rth), the voltage across the load is Vth/2, and the load power becomes Pmax = Vth^2/(4Rth). If RL is either 0 (short) or infinite (open), the load power is zero, so those cases aren’t optimal. Therefore, matching the load to the source resistance delivers the greatest power.