Six resistors of 3 Ωeach are connected along the sides of a...

Six resistors of $3 \Omega$ each are connected along the sides of a hexagon and three resistors of $6 \Omega$ each are connected along $\mathrm{AC}, \mathrm{AD}$, and $\mathrm{AE}$ as shown in the figure. The equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is equal to: (A) $3 \Omega$ (B) $9 \Omega$ (C) $2 \Omega$ (D) $16 \Omega$

Six resistors of $3 \Omega$ each are connected along the sides of a hexagon and three resistors of $6 \Omega$ each are connected along $\mathrm{AC}, \mathrm{AD}$, and $\mathrm{AE}$ as shown in the figure. The equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is equal to:
(A) $3 \Omega$
(B) $9 \Omega$
(C) $2 \Omega$
(D) $16 \Omega$

Key Concepts

Resistor Network Analysis

Resistor network analysis involves applying circuit reduction techniques such as combining series and parallel resistors, and sometimes further transformations, to determine characteristics like the equivalent resistance of the circuit. This approach is essential for solving circuit problems in both theoretical and practical electronics.

Circuit Symmetry

Circuit symmetry is used when parts of the circuit are mirror images or have uniform structure, allowing the simplification of complex networks. Recognizing symmetry can reduce the number of unique paths to analyze, thus streamlining the process of finding equivalent resistances or other circuit parameters.

Equivalent Resistance

The concept of equivalent resistance refers to the single resistance that can replace an entire resistor network while preserving the same overall electrical behavior. This makes it simpler to analyze complex circuits, especially when determining current flow or voltage drop across the network.

Series and Parallel Resistor Combinations

Series and parallel combinations are fundamental methods used to simplify resistor networks. In series, resistors add directly because the same current flows through each; in parallel, the reciprocals of the resistances add because each resistor is subjected to the same voltage. These methods help in systematically reducing complex networks to simpler equivalent circuits.

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