Thevenin's Theorem

• $V_{th}$ — the open-circuit voltage at the terminals.
• $R_{th}$ — the resistance seen at the terminals with all independent sources turned off (or $R_{th} = V_{oc}/I_{sc}$).

Example: 12 V with a divider of 4 kΩ (top) and 12 kΩ (bottom):

$V_{th} = 12 \times \frac{12}{16} = 9\ \text{V} \qquad R_{th} = 4 \parallel 12 = 3\ \text{k}\Omega$

The load current for any load is then simply $I = V_{th}/(R_{th} + R_L)$ — no need to re-solve the whole circuit.