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 bc?

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Identify the resistors in the triangular array: 18.0 Ω, 22.0 Ω, and 13.0 Ω.

Since the battery is connected across points b and c, determine which resistors are in series or parallel between these points.

Calculate the equivalent resistance of the resistors between points b and c. If resistors are in series, add their resistances. If in parallel, use the formula: 1/R_eq = 1/R1 + 1/R2 + ...

Once the equivalent resistance (R_eq) is found, use Ohm's Law to find the current drawn from the battery: I = V/R_eq, where V is the voltage of the battery (35.0 V).

Substitute the known values into the equation to solve for the current I, ensuring all units are consistent.

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주요 개념

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Ohm's Law

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

Series and Parallel Circuits

In a series circuit, resistors are arranged in a single path, so the same current flows through each resistor. The total resistance is the sum of individual resistances. In a parallel circuit, resistors are connected across the same two points, providing multiple paths for the current. The total resistance in a parallel circuit is found using the reciprocal formula: 1/R_total = 1/R1 + 1/R2 + ... + 1/Rn. Understanding these configurations is crucial for analyzing complex circuits.

Kirchhoff's Voltage Law

Kirchhoff's Voltage Law (KVL) states that the sum of the electrical potential differences (voltage) around any closed network is zero. This principle is used to analyze the voltage drops across components in a circuit loop, ensuring that the total voltage supplied by sources equals the total voltage drop across the resistors. KVL is vital for solving circuits with multiple loops and branches, as it helps in setting up equations to find unknown values.