Ch 26: Direct-Current Circuits

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 26: Direct-Current Circuits

Problem 31b

Chapter 26, Problem 31b

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Related Practice

Textbook Question

The 10.00 V battery in Fig. E26.28 is removed from the circuit and reinserted with the opposite polarity, so that its positive terminal is now next to point a. The rest of the circuit is as shown in the figure. Find the current in each branch.

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Textbook Question

In the circuit shown in Fig. E26.34, the 6.0 Ω resistor is consuming energy at a rate of 24 J/s when the current through it flows as shown. What are the polarity and emf ε of the unknown battery, assuming it has negligible internal resistance?

Textbook Question

The 5.00 V battery in Fig. E26.28 is removed from the circuit and replaced by a 15.00 V battery, with its negative terminal next to point b. The rest of the circuit is as shown in the figure. Find the current in each branch.

Textbook Question

An emf source with ε = 120V, a resistor with R = 80.0Ω, and a capacitor with C = 4.00 μF are connected in series. As the capacitor charges, when the current in the resistor is 0.900 A, what is the magnitude of the charge on each plate of the capacitor?

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Textbook Question

In the circuit shown in Fig. E26.27 find the unknown emfs $epsilon sub 1$ and $epsilon sub 2$ .

Textbook Question

In the circuit shown in Fig. E26.33 all meters are idealized and the batteries have no appreciable internal resistance. Find the reading of the voltmeter with the switch S open. Which point is at a higher potential: a or b?