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 30
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 .
Verified step by step guidance1
Identify the components in the circuit: two batteries with emfs of 12.0 V and 5.0 V, internal resistances of 1.85 Ω and 1.25 Ω, and resistors of 8.50 Ω, 4.50 Ω, and 15.0 Ω.
Apply Kirchhoff's loop rule to the circuit. Choose a loop that includes points a and c, and write the equation for the sum of potential differences around the loop. Consider the direction of current flow and the polarity of the batteries.
Calculate the current in the circuit using the loop equation. You may need to solve a system of equations if there are multiple loops. Use Ohm's law, \( V = IR \), where \( V \) is the voltage, \( I \) is the current, and \( R \) is the resistance.
Determine the potential difference across each component between points a and c. For resistors, use \( V = IR \). For batteries, consider the emf and internal resistance.
Sum the potential differences from point a to point c to find \( V_{ac} \). Remember to account for the direction of current and the sign of each potential difference.
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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 around any closed loop in a circuit must equal zero. This principle is based on the conservation of energy, ensuring that the energy supplied by the batteries is equal to the energy used by the resistors and any other components. Applying this rule helps determine unknown voltages or currents in complex circuits.
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Intro to Kirchhoff's Loop Rule
Electromotive Force (EMF) and Internal Resistance
Electromotive force (EMF) is the voltage generated by a battery or power source when no current flows. However, real batteries have internal resistance, which causes a voltage drop when current flows. The effective voltage across the battery terminals is the EMF minus the voltage drop due to internal resistance, affecting the total potential difference in the circuit.
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09:57Motional EMF
Potential Difference
Potential difference, or voltage, between two points in a circuit is the work done to move a unit charge from one point to another. It is measured in volts and is crucial for understanding how energy is transferred in a circuit. Calculating the potential difference between points a and c involves considering the contributions from resistors and batteries along the path.
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07:04Potential Difference Between Two Charges
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
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.
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Textbook Question
An idealized ammeter is connected to a battery as shown in Fig. E. Find the reading of the ammeter.
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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
An idealized ammeter is connected to a battery as shown in Fig. E. Find the current through the - resistor.
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