The batteries shown in the circuit in Fig. E26.24 have negligibly small internal resistances. Find the current through the 30.0-Ω resistor.

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Identify the components in the circuit: two batteries (E1 and E2) and two resistors (R1 and R2). The resistors are labeled with their resistance values, R1 = 30.0 Ω and R2 = unknown.

Apply Kirchhoff's loop rule to the circuit. This rule states that the sum of the electromotive forces (emf) in any closed loop is equal to the sum of the potential drops (voltage) across the resistors in that loop.

Write the equation for the loop using Kirchhoff's rule: E1 - I * R1 - E2 - I * R2 = 0, where I is the current through the resistors.

Rearrange the equation to solve for the current I: I = (E1 - E2) / (R1 + R2).

Substitute the known values into the equation. You have R1 = 30.0 Ω, and you need to know the values of E1, E2, and R2 to find the current I through the 30.0 Ω resistor.

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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 through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance. It is mathematically expressed as I = V/R, where I is the current, V is the voltage, and R is the resistance. This law is crucial for calculating the current in circuits.

Kirchhoff's Loop Rule

Kirchhoff's Loop Rule, also known as Kirchhoff's Voltage Law, states that the sum of the electromotive forces (emf) and potential differences (voltage) around any closed loop in a circuit is zero. This principle is essential for analyzing complex circuits, as it allows for the calculation of unknown currents and voltages by setting up equations based on the conservation of energy within the loop.

Series and Parallel Circuits

In a series circuit, components are connected end-to-end, so the same current flows through each component, and the total resistance is the sum of individual resistances. In a parallel circuit, components are connected across the same voltage source, and the total current is the sum of the currents through each component. Understanding these configurations is vital for analyzing how current and voltage distribute in a circuit.