Ch 25: Current, Resistance, and EMF

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 25: Current, Resistance, and EMF

Problem 39b

Chapter 25, Problem 39b

Consider the circuit of Fig. E25.30. What is the power output of the 16.0 V battery?

Verified step by step guidance

Identify the components in the circuit: The circuit consists of three batteries with voltages of 16.0 V, 13.5 V, and 7.5 V, and resistors with resistances of 2.2 Ω, 1.0 Ω, 8.0 Ω, and 6.0 Ω.

Apply Kirchhoff's loop rule: The sum of the potential differences (voltage) around any closed loop in a circuit must be zero. Write the equation for the loop considering the direction of current flow and the polarity of the batteries.

Calculate the total resistance in the circuit: Add up the resistances of the resistors in series to find the total resistance. The resistors are in series, so the total resistance R_total = 2.2 Ω + 1.0 Ω + 8.0 Ω + 6.0 Ω.

Determine the current in the circuit: Use Ohm's Law, V = IR, where V is the net voltage from the batteries, I is the current, and R is the total resistance. Solve for the current I.

Calculate the power output of the 16.0-V battery: Use the formula P = IV, where P is the power, I is the current calculated in the previous step, and V is the voltage of the 16.0-V battery.

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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 fundamental in circuit analysis, 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 expressed as V = IR, and is essential for calculating current in the circuit, which is needed to determine the power output of the battery.

Power in Electrical Circuits

Power in electrical circuits is the rate at which energy is transferred or converted. It is calculated using the formula P = VI, where P is power, V is voltage, and I is current. Understanding this concept is crucial for determining the power output of the battery, as it involves calculating the product of the battery's voltage and the current flowing through the circuit.

Kirchhoff's Voltage Law

Kirchhoff's Voltage Law states that the sum of the electrical potential differences (voltage) around any closed network is zero. This principle is used to analyze the circuit by ensuring that the sum of the voltages provided by the batteries equals the sum of the voltage drops across the resistors, allowing for the calculation of current and subsequently the power output of the battery.

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Kirchhoff's Junction Rule

Related Practice

Textbook Question

When a resistor with resistance $R$ is connected to a $1.50$ -V flashlight battery, the resistor consumes $0.0625$ W of electrical power. (Throughout, assume that each battery has negligible internal resistance.) What power does the resistor consume if it is connected to a $12.6$ -V car battery? Assume that $R$ remains constant when the power consumption changes.

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Textbook Question

The circuit shown in Fig. E $25.33$ contains two batteries, each with an emf and an internal resistance, and two resistors. Find the terminal voltage $V_{a b}$ of the $16.0$ -V battery.

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Textbook Question

Consider the circuit of Fig. E25.30 Show that the power output of the 16.0 V battery equals the overall rate of consumption of electrical energy in the rest of the circuit.

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Textbook Question

Consider the circuit of Fig. E25.30. What is the total rate at which electrical energy is dissipated in the 5.0 Ω and 9.0 Ω resistors?

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Textbook Question

Consider the circuit of Fig. E25.30. At what rate is electrical energy being converted to other forms in the 8.0 V battery?

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Textbook Question

Electric eels generate electric pulses along their skin that can be used to stun an enemy when they come into contact with it. Tests have shown that these pulses can be up to 500 V and produce currents of 80 mA (or even larger). A typical pulse lasts for 10 ms. What power and how much energy are delivered to the unfortunate enemy with a single pulse, assuming a steady current?