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 39c

Chapter 25, Problem 39c

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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Identify the components in the circuit: The circuit consists of resistors with resistances of 2.85 Ω, 1.25 Ω, 9.50 Ω, 5.50 Ω, and 6.50 Ω, and two batteries with voltages of 20.0 V and 6.0 V.

Determine the total resistance in the circuit: Add the resistances of all resistors in series to find the total resistance. Use the formula R_total = R1 + R2 + R3 + R4 + R5.

Calculate the total voltage in the circuit: Since the batteries are in series, subtract the voltage of the 6.0 V battery from the 20.0 V battery to find the net voltage. Use the formula V_net = V1 - V2.

Use Ohm's Law to find the current in the circuit: Apply the formula I = V_net / R_total, where I is the current, V_net is the net voltage, and R_total is the total resistance.

Calculate the power converted by the 8.0 V battery: Use the formula P = V_battery * I, where P is the power, V_battery is the voltage of the battery, and I is the current through the 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 crucial for calculating current in the circuit, which is needed to determine the power conversion rate in the battery.

Power in Electrical Circuits

Power in electrical circuits is the rate at which energy is converted from electrical energy to other forms, such as heat or light. It is calculated using the formula P = VI, where P is power, V is voltage, and I is current. Understanding this concept is essential for determining the rate at which the 8.0-V battery converts electrical energy into other forms.

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 helps in analyzing complex circuits by allowing the calculation of unknown voltages and currents, which is necessary for understanding how the 8.0-V battery interacts with other components in the circuit.

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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

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?

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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

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?

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