Find the equivalent resistance looking into terminals a-b...

Find the equivalent resistance looking into terminals $a-b$ for the network shown in Figure P2.61. (Hint: First, connect a 1-A current source across terminals $a$ and $b$. Then, solve the network by the node-voltage technique. The voltage across the current source is equal in value to the equivalent resistance.

Key Concepts

Equivalent Resistance

Equivalent resistance is the resistance that can replace an entire network to produce the same voltage-current relationship at a pair of terminals. It simplifies circuit analysis by allowing the network to be represented as a single resistor, which is especially useful when determining load effects or analyzing power distribution in a circuit.

Test Source Method

The test source method involves injecting a known independent source (voltage or current) into the circuit’s output terminals and calculating the resulting voltage or current response. This response is then used to determine the equivalent impedance, which, in the case of purely resistive circuits, is the equivalent resistance. This method is central in circuit analysis when all internal sources are deactivated or when analyzing passive networks.

Node-Voltage Technique

The node-voltage technique is an analytical method used in circuit analysis that assigns voltage variables to the nodes of a circuit relative to a common reference point (ground). By applying Kirchhoff’s Current Law (KCL) at each node, a set of simultaneous equations is formed. Solving these equations allows for the determination of unknown node voltages, which can then be used to compute other circuit parameters such as currents and equivalent resistance.

Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law is a fundamental principle in electrical circuit theory stating that the algebraic sum of currents entering a node must equal the sum of currents leaving that node. This law is critical in applying the node-voltage technique because it provides the necessary equations to solve for the unknown node voltages across the circuit.

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