Textbook Question
Compared to an ideal battery, by what percentage does the battery's internal resistance reduce the potential difference across the 20 Ω resistor in FIGURE EX28.24?
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Ch 28: Fundamentals of Circuits
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 28, Problem 30
In FIGURE EX28.30, what is the value of the potential at points 1 and 2?
Verified step by step guidance1
Step 1: Analyze the circuit diagram. The circuit consists of two batteries (15 V and 5 V), two resistors (4 Ω and 1 Ω), and two points (1 and 2) where the potential needs to be calculated. The circuit is a closed loop, and Kirchhoff's Voltage Law (KVL) will be applied.
Step 2: Apply Kirchhoff's Voltage Law (KVL) to the loop. KVL states that the sum of the potential differences (voltage drops and rises) around any closed loop is zero. Write the equation for the loop considering the direction of current flow and the polarity of the batteries.
Step 3: Calculate the current in the circuit. Use Ohm's Law, \( V = IR \), to find the current. The total resistance in the circuit is the sum of the resistances (4 Ω + 1 Ω = 5 Ω). The net voltage driving the current is the difference between the two batteries (15 V - 5 V = 10 V). Solve for current using \( I = \frac{V}{R} \).
Step 4: Determine the potential at point 1. Start from the 15 V battery and move through the circuit to point 1. Account for the voltage drop across the 4 Ω resistor using \( V_{drop} = IR \). Subtract this drop from the battery voltage to find the potential at point 1.
Step 5: Determine the potential at point 2. Start from the 15 V battery and move through the circuit to point 2. Account for the voltage drop across both resistors (4 Ω and 1 Ω) using \( V_{drop} = IR \). Subtract these drops from the battery voltage to find the potential at point 2.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Electric Potential
Electric potential, often referred to as voltage, is the amount of electric potential energy per unit charge at a specific point in an electric field. It is measured in volts (V) and indicates the work done to move a charge from a reference point to the point in question. Understanding how potential varies in a circuit is crucial for analyzing the behavior of electrical components.
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Electric Potential
Ohm's Law
Ohm's Law states that the current (I) flowing 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. This relationship is expressed as V = IR. It is fundamental for calculating current, voltage, and resistance in electrical circuits, which is essential for determining potential at different points.
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Series and Parallel Circuits
In electrical circuits, components can be arranged in series or parallel configurations. In a series circuit, the same current flows through all components, while in a parallel circuit, the voltage across each component is the same. Understanding these configurations is vital for analyzing how voltage is distributed across components, which directly affects the potential at various points in the circuit.
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Related Practice
Textbook Question
What is the time constant for the discharge of the capacitors in FIGURE EX28.34?
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Textbook Question
Show that the product RC has units of s.
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Textbook Question
Two of the three resistors in FIGURE EX28.23 are unknown but equal. The total resistance between points 1 and 2 is 75Ω. What is the value of R?
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Textbook Question
What is the equivalent resistance between points 1 and 2 in FIGURE EX28.27?
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Textbook Question
A capacitor is discharged through a 100 Ω resistor. The discharge current decreases to 25% of its initial value in 2.5 ms. What is the value of the capacitor?
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