Q12Basic Electrical Engineering

Question

Q.2. State Thevenin's theorem and give a proof. Apply this theorem to calculate the current passing through the 4 Ω resistor of the circuit of Fig. 1.

Answer 1

Statement of Thevenin's Theorem: It states that any complex, two-terminal, linear bilateral DC network containing multiple independent voltage and current sources and resistances can be replaced by a single equivalent electrical circuit consisting of an ideal voltage source ( $V_{t h}$ ) connected in series with a single equivalent resistance ( $R_{t h}$ ).

$V_{t h}$ (Thevenin Voltage): This is the open-circuit voltage measured across the two terminals (A and B) when the load resistor ( $R_{L}$ ) is completely removed from the circuit.
$R_{t h}$ (Thevenin Resistance): This is the equivalent resistance looking back into the terminals A and B with all independent power sources deactivated (ideal voltage sources replaced by short circuits, ideal current sources replaced by open circuits).

Application (Proof Concept): Once the complex network is reduced to the Thevenin equivalent circuit, any load resistor $R_{L}$ can be reconnected across the terminals. The current flowing through that specific branch can be easily calculated using a simple series Ohm's law equation:

I_{L} = \frac{V _{t h}}{R _{t h} + R _{L}}

This theorem drastically reduces the computational workload when analyzing how changes in one specific branch (the load) affect the current, without needing to repeatedly solve mesh or nodal equations for the entire complex network.

Q12Basic Electrical Engineering

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