Textbook Question
The circuit shown in Fig. E contains two batteries, each with an emf and an internal resistance, and two resistors. Find the current in the circuit (magnitude and direction).
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Ch 25: Current, Resistance, and EMF
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 25, Problem 33b
The circuit shown in Fig. E contains two batteries, each with an emf and an internal resistance, and two resistors. Find the terminal voltage of the -V battery.
Verified step by step guidance1
Identify the components in the circuit: two batteries with emfs of 9.0 V and 4.0 V, internal resistances of 1.5 Ω and 1.0 Ω respectively, and two external resistors of 10.0 Ω and 5.5 Ω.
Apply Kirchhoff's loop rule to the circuit. Start at one point in the loop and move around the circuit, adding the emfs and subtracting the voltage drops across resistors. The sum should equal zero.
Express the voltage drop across each resistor using Ohm's Law, V = IR, where I is the current through the resistor and R is its resistance.
Set up the equation for the loop: 9.0 V - I(1.5 Ω) - I(10.0 Ω) - 4.0 V - I(1.0 Ω) - I(5.5 Ω) = 0. Solve this equation for the current I.
Calculate the terminal voltage Vab of the 9.0 V battery using the formula Vab = emf - Ir, where emf is the electromotive force of the battery and r is its internal resistance. Substitute the values to find Vab.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Kirchhoff's Loop Rule
Kirchhoff's Loop Rule states that the sum of the potential differences (voltage) around any closed loop in a circuit must equal zero. This principle is essential for analyzing circuits with multiple loops and components, as it allows us to set up equations that relate the emfs, resistances, and currents in the circuit. Applying this rule helps determine unknown values such as current or voltage across specific elements.
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Intro to Kirchhoff's Loop Rule
Terminal Voltage
Terminal voltage is the voltage output of a battery, measured across its terminals, and is affected by the internal resistance of the battery. It is calculated by subtracting the voltage drop due to the internal resistance from the emf of the battery. Understanding terminal voltage is crucial for determining the actual voltage available to the external circuit, which can differ from the battery's emf due to internal losses.
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Internal Resistance
Internal resistance is the inherent resistance within a battery that causes a voltage drop when current flows through it. This resistance affects the terminal voltage and efficiency of the battery. In circuit analysis, internal resistance is considered to calculate the actual voltage supplied to the circuit and the power dissipated within the battery itself, impacting the overall performance of the circuit.
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Related Practice
Textbook Question
When a resistor with resistance is connected to a -V flashlight battery, the resistor consumes 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 -V car battery? Assume that remains constant when the power consumption changes.
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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
The circuit shown in Fig. E contains two batteries, each with an emf and an internal resistance, and two resistors. Find the potential difference of point with respect to point .
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Textbook Question
An idealized ammeter is connected to a battery as shown in Fig. E. Find the terminal voltage of the battery.
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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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