Use Thévenin's theorem to find Io in the network in Fig....

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Key Concepts

Thévenin's Theorem

Thévenin's Theorem states that any linear electrical network with voltage and current sources and only resistances can be replaced at terminals A–B by an equivalent voltage source (V_th) in series with an equivalent resistance (R_th). This simplifies circuit analysis, especially when studying the effect of varying load conditions.

Open-Circuit (Thévenin) Voltage

The open-circuit voltage (V_th) is the voltage measured between the output terminals when no load is connected. It represents the ideal voltage source's magnitude in the Thévenin equivalent circuit.

Thévenin Equivalent Resistance

The Thévenin equivalent resistance (R_th) is determined by deactivating all independent sources (replacing voltage sources with short circuits and current sources with open circuits) and calculating the resistance seen across the output terminals. This resistance, in series with the open-circuit voltage, models the original network’s behavior for load analysis.

Load Current Calculation

Once the Thévenin equivalent circuit is established, the load current (I_o) can be easily computed by applying Ohm’s Law. The load resistor is connected across the V_th and R_th series combination, and the current through the load is calculated as I_o = V_th / (R_th + R_load), thereby simplifying the original complex circuit analysis.

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