Three 6-ohm resistors are arranged in a triangle as shown. A...

Three 6-ohm resistors are arranged in a triangle as shown. A voltage source of 12 V is impressed across one of the resistors. (a) How much current is in that resistor? (b) How much current is in each of the other two resistors? (c) How much current is in the voltage source? (d) What is the equivalent resistance of the circuit (what single resistor connected to the voltage source could replace the three resistors)?

Three 6-ohm resistors are arranged in a triangle as shown. A voltage source of 12 V is impressed across one of the resistors.
(a) How much current is in that resistor?
(b) How much current is in each of the other two resistors?
(c) How much current is in the voltage source?
(d) What is the equivalent resistance of the circuit (what single resistor connected to the voltage source could replace the three resistors)?

Key Concepts

Delta (?) Network Analysis

A delta network is a configuration where resistors are arranged in a triangle. Analyzing such networks often involves recognizing the symmetry or applying transformation techniques like the Delta-to-Wye (?-Y) transformation. This method converts the triangle of resistors into an equivalent star (or Y) network, simplifying the circuit into combinations of series and parallel resistors for easier computation of currents and voltages.

Equivalent Resistance

Equivalent resistance is the single resistance that can replace a complex combination of resistors without altering the overall behavior of the circuit. This concept is central in circuit analysis as it allows one to reduce a network to a single resistor to simplify computations, especially when determining how a voltage source interacts with the entire circuit.

Kirchhoff's Laws

These are fundamental rules used in circuit analysis. Kirchhoff's Current Law (KCL) states that the total current entering a node equals the total current leaving it, while Kirchhoff's Voltage Law (KVL) states that the sum of the electrical potential differences (voltages) around any closed network is zero. They are essential for setting up the equations that govern the currents and voltages in a circuit, regardless of its configuration.

Series and Parallel Resistor Combinations

Understanding how resistors combine when connected in series or in parallel is crucial for simplifying complex circuits. In series, resistances add directly, whereas in parallel, the reciprocal of the equivalent resistance is the sum of the reciprocals of the individual resistances. This concept helps to transform part of the circuit into an equivalent resistor, making the analysis of the overall circuit more straightforward.

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