### Equivalent Circuits

**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.