In the circuit shown in Fig. E26.31 the batteries have negligible internal resistance and the meters are both idealized. With the switch S open, the voltmeter reads 15.0 V. What will the ammeter read when the switch is closed?

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Identify the components in the circuit: There are two batteries, one with an unknown emf (E) and another with 52.0 V. The resistors are 10.0 Ω, 18.0 Ω, 40.0 Ω, 14.0 Ω, and 25.0 Ω. The voltmeter reads 15.0 V when the switch is open.

Calculate the total resistance in the circuit when the switch is closed. The 18.0 Ω and 40.0 Ω resistors are in series, and their equivalent resistance is R1 = 18.0 Ω + 40.0 Ω. The 14.0 Ω and 25.0 Ω resistors are also in series, with an equivalent resistance of R2 = 14.0 Ω + 25.0 Ω.

Determine the total resistance in the circuit. The resistors R1 and R2 are in parallel, so their combined resistance is given by 1/R_parallel = 1/R1 + 1/R2. Add the 10.0 Ω resistor in series to find the total resistance R_total = 10.0 Ω + R_parallel.

Use Kirchhoff's loop rule to find the current through the circuit. The loop rule states that the sum of the emfs in any closed loop is equal to the sum of the potential drops (IR) across the resistors. Set up the equation: E - I * R_total = 0, where E is the total emf (52.0 V + E).

Solve for the current I using the equation from the previous step. The current I is what the ammeter will read when the switch is closed. Rearrange the equation to find I = E / R_total.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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 V = IR. This law is crucial for calculating the current in the circuit when the switch is closed.

Series and Parallel Circuits

In a series circuit, components are connected end-to-end, so the same current flows through each component. In a parallel circuit, components are connected across the same voltage source, so the voltage across each component is the same. Understanding these configurations is essential for analyzing the circuit's total resistance and the current distribution when the switch is closed.

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 helps in analyzing the circuit by ensuring that the total voltage supplied by the batteries equals the sum of the voltage drops across the resistors, which is necessary to determine the current through the ammeter when the switch is closed.