How it works
Thevenin's theorem: any linear two-terminal network can be replaced by a voltage source V_th (= open-circuit voltage across the terminals) in series with a resistance R_th (= resistance seen from the terminals with all independent sources deactivated). Deactivating means replacing voltage sources with short circuits and current sources with open circuits. Norton's theorem: the same network can be replaced by a current source I_N = V_th/R_th in parallel with R_th. The Norton current I_N equals the short-circuit current at the terminals. Source transformation between Thevenin and Norton: V_th = I_N × R_th.
Key points to remember
For circuits with dependent sources only, R_th cannot be found by source deactivation — instead, apply a test voltage V_x at terminals, find the resulting current I_x, then R_th = V_x/I_x. When both independent and dependent sources are present, use V_th = V_oc and then apply test source method for R_th. Maximum power transfer: load receives maximum power P_max = V_th²/(4R_th) when R_L = R_th. The Thevenin resistance equals the Norton resistance: R_th = R_N. A practical voltage source (V_s, R_s) is equivalent to a practical current source (I_s = V_s/R_s, R_s in parallel) — this source transformation is applied repeatedly in ladder network simplification.
Exam tip
The examiner always asks you to find the Thevenin equivalent of a circuit containing a dependent source — show the open-circuit voltage calculation and the test-source method for R_th as two clearly separated steps, because combining them in one step loses marks.