State the condition of maximum power transfer in a circuit and write the expression for maximum power.

Condition: a linear DC network delivers maximum power to a load resistance R_L when the load resistance is equal to the Thevenin (internal) resistance of the network seen from the load terminals: R_L = R_th.

Load power \( P_L = \dfrac{V_{th}^2R_L}{(R_{th}+R_L)^2} \); setting dP_L/dR_L = 0 gives R_L = R_th.

Maximum power: \[ P_{max} = \frac{V_{th}^2}{4R_{th}} \quad\left(= \frac{I_N^2R_N}{4}\right) \]

Efficiency at maximum power transfer is 50%. (For AC circuits the condition is Z_L = Z_th*, the complex conjugate.)