A triangular array of resistors is shown in Fig. E26.5. What current will this array draw from a 35.0 V battery having negligible internal resistance if we connect it across ac?

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Identify the resistors in the circuit that are connected between points a and c. In this case, the resistors are 14.0 Ω, 8.0 Ω, and 15.0 Ω.

Determine the configuration of these resistors. The 14.0 Ω and 8.0 Ω resistors are in series, and their combination is in parallel with the 15.0 Ω resistor.

Calculate the equivalent resistance of the 14.0 Ω and 8.0 Ω resistors in series using the formula: R_series = R1 + R2. Substitute R1 = 14.0 Ω and R2 = 8.0 Ω.

Calculate the total equivalent resistance of the circuit by finding the parallel combination of the series resistance (from step 3) and the 15.0 Ω resistor using the formula: 1/R_parallel = 1/R_series + 1/R3. Substitute R3 = 15.0 Ω.

Use Ohm's Law to find the current drawn from the battery. Ohm's Law states that I = V/R_total, where V is the voltage of the battery (35.0 V) and R_total is the total equivalent resistance calculated in step 4.

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주요 개념

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Ohm's Law

Ohm's Law is a fundamental principle in electronics that states the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. It is expressed as I = V/R, where I is the current, V is the voltage, and R is the resistance. This law is essential for calculating the current in the circuit when the voltage and resistance are known.

Series and Parallel Circuits

In electrical circuits, resistors can be arranged in series or parallel configurations. In a series circuit, resistors are connected end-to-end, and the total resistance is the sum of individual resistances. In a parallel circuit, resistors are connected across the same two points, and the total resistance is found using the reciprocal formula: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn. Understanding these configurations is crucial for determining the equivalent resistance in complex circuits.

Kirchhoff's Circuit Laws

Kirchhoff's Circuit Laws consist of two rules: the Junction Rule and the Loop Rule. The Junction Rule states that the total current entering a junction equals the total current leaving it, ensuring charge conservation. The Loop Rule states that the sum of the voltage gains and losses around any closed loop in a circuit must be zero. These laws are vital for analyzing circuits with multiple loops and branches, helping to solve for unknown currents and voltages.