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 39d

Chapter 25, Problem 39d

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.

Verified step by step guidance

Identify the components in the circuit and their respective values, including resistances, currents, and voltages. This will help in understanding how the circuit is configured and how the power is distributed.

Use Ohm's Law, which states \( V = IR \), to calculate the current flowing through each resistor. This requires knowing the total resistance in the circuit and the voltage provided by the battery.

Calculate the power output of the battery using the formula \( P = IV \), where \( I \) is the current through the battery and \( V \) is the voltage of the battery. This gives the total power supplied by the battery.

Determine the power consumed by each resistor using the formula \( P = I^2R \), where \( I \) is the current through the resistor and \( R \) is the resistance. Sum the power consumed by all resistors to find the total power consumption in the circuit.

Verify that the total power output of the battery equals the total power consumed by the resistors. This confirms that the power supplied by the battery is equal to the power consumed in the circuit, demonstrating energy conservation.

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Key Concepts

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

Conservation of Energy in Electrical Circuits

The principle of conservation of energy states that energy cannot be created or destroyed, only transformed. In electrical circuits, this means the total power supplied by sources, like batteries, must equal the total power consumed by the circuit components, such as resistors. This balance ensures that all energy input is accounted for in the form of heat, light, or other energy forms.

Power in Electrical Circuits

Power in electrical circuits is the rate at which energy is transferred or converted. It is calculated as the product of voltage and current (P = VI). For a battery, the power output is determined by its voltage and the current it supplies. Understanding power is crucial for analyzing how energy is distributed and consumed within a circuit.

Ohm's Law and Circuit Analysis

Ohm's Law relates voltage (V), current (I), and resistance (R) in a circuit through the equation V = IR. This fundamental relationship helps in analyzing circuits by allowing the calculation of current flow and voltage drops across components. Applying Ohm's Law is essential for determining how the power supplied by a battery is distributed across the circuit elements.

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Related Practice

Textbook Question

A heart defibrillator is used to enable the heart to start beating if it has stopped. This is done by passing a large current of 12 A through the body at 25 V for a very short time, usually about 3.0 ms. How much energy is transferred?

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Textbook Question

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

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

The battery for a certain cell phone is rated at 3.70 V. According to the manufacturer, it can produce 3.15 × 10⁴ J of electrical energy, enough for 5.25 h of operation, before needing to be recharged. Find the average current that this cell phone draws when turned on.

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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?