Correct Answer - Option 2 : Thevenin's equivalent circuit
APPLICATION OF THEVENIN THEOREM-
Thevenin's Theorem is useful in analyzing power systems and other circuits where one particular resistor in the circuit (called the “load” resistor) is subject to change, and re-calculation of the circuit is necessary with each trial value of load resistance, to determine the voltage across it and current.
In the question it is clearly given Branch resistor is varying so Thevenin equivalent circuit will be the correct answer.
NOTE- We can also use Norton equivalent circuits in these types of circuits.
1. When in a circuit with more than one supply present then we use the Superposition Theorem.
2. Mesh analysis is a method that is used to solve planar circuits for the currents (and indirectly the voltages) at any place in the electrical circuit.
3. Nodal Analysis is a method that is used to solve planar circuits for the voltages (and indirectly the currents) at any place in the electrical circuit.