Equivalent Circuits - JEE / CBSE Board Exam - Remember these Concepts

1. Concept of equivalent resistance and combining resistors in series and parallel.

• Series combination:* Resistors are connected end to end, with the same current flowing through each resistor. The total resistance of a series combination is the sum of the individual resistances.
• Parallel combination:* Resistors are connected side by side, with the same voltage applied to each resistor. The total resistance of a parallel combination is given by:

1/R = 1/R1 + 1/R2 + 1/R3 + ...

2. Nodal analysis and mesh analysis for solving complex circuits.

• Nodal analysis: A method of solving circuits by assigning voltages to nodes (points where two or more components are connected) and using Ohm’s law to find the currents through the components.
• Mesh analysis: A method of solving circuits by assigning currents to loops (closed paths in the circuit) and using Kirchhoff’s voltage law to find the voltages across the components.

3. Thevenin’s theorem and the concept of a Thevenin equivalent circuit.

• Thevenin’s theorem: Any linear circuit can be represented by a single voltage source in series with a single resistor. The voltage source is equal to the open-circuit voltage of the circuit, and the resistor is equal to the internal resistance of the circuit.
• Thevenin equivalent circuit: A circuit that consists of a voltage source in series with a resistor, which is equivalent to a given linear circuit.

4. Norton’s theorem and the concept of a Norton equivalent circuit.

• Norton’s theorem: Any linear circuit can be represented by a single current source in parallel with a single resistor. The current source is equal to the short-circuit current of the circuit, and the resistor is equal to the internal resistance of the circuit.
• Norton equivalent circuit: A circuit that consists of a current source in parallel with a resistor, which is equivalent to a given linear circuit.

5. Superposition theorem and superposition principle.

• Superposition theorem: The current or voltage in a linear circuit is the sum of the currents or voltages that would be produced if each independent source in the circuit were acting alone.
• Superposition principle: A method of solving circuits by finding the current or voltage that would be produced by each independent source in the circuit, and then adding the results together.

6. Maximum power transfer theorem and circuit conditions for maximum power transfer.

• Maximum power transfer theorem: The maximum power is transferred from a source to a load when the load resistance is equal to the internal resistance of the source.
• Circuit conditions for maximum power transfer: The load resistance is equal to the internal resistance of the source.