Textbook Question
A 4.5-V battery is connected to a bulb whose resistance is 2.3 Ω. How many electrons leave the battery per minute?
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Ch. 25 - Electric Current and Resistance
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179
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Table of contents
- Ch. 01 - Introduction, Measurement, Estimating10
- Ch. 02 - Describing Motion: Kinematics in One Dimension30
- Ch. 03 - Kinematics in Two or Three Dimensions; Vectors15
- Ch. 04 - Dynamics: Newton's Laws of Motion16
- Ch. 05 - Using Newton's Laws: Friction, Circular Motion, Drag Forces22
- Ch. 06 - Gravitation and Newton's Synthesis10
- Ch. 07 - Work and Energy21
- Ch. 08 - Conservation of Energy33
- Ch. 09 - Linear Momentum26
- Ch. 10 - Rotational Motion41
- Ch. 11 - Angular Momentum; General Rotation27
- Ch. 12 - Static Equilibrium; Elasticity and Fracture27
- Ch. 13 - Fluids28
- Ch. 14 - Oscillations14
- Ch. 15 - Wave Motion35
- Ch. 16 - Sound5
- Ch. 17 - Temperature, Thermal Expansion, and the Ideal Gas Law40
- Ch. 18 - Kinetic Theory of Gases18
- Ch. 19 - Heat and the First Law of Thermodynamics31
- Ch. 20 - Second Law of Thermodynamics32
- Ch. 21 - Electric Charge and Electric Field7
- Ch. 23 - Electric Potential20
- Ch. 24 - Capacitance, Dielectrics, Electric Energy, Storage15
- Ch. 25 - Electric Current and Resistance32
- Ch. 26 - DC Circuits22
- Ch. 27 - Magnetism21
- Ch. 28 - Sources of Magnetic Field24
- Ch. 29 - Electromagnetic Induction and Faraday's Law21
- Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits42
- Ch. 31 - Maxwell's Equations and Electromagnetic Waves25
- Ch. 32 - Light: Reflection and Refraction42
- Ch. 33 - Lenses and Optical Instruments21
- Ch. 34 - The Wave Nature of Light: Interference and Polarization26
- Ch. 35 - Diffraction24
- Ch. 36 - The Special Theory of Relativity29
- Ch. 38 - Quantum Mechanics1
- Ch. 40 - Molecules and Solids6
- Ch. 43 - Elementary Particles3
- Ch. 44 - Astrophysics and Cosmology9
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Not the one you use?Change textbook
Chapter 24, Problem 7
(a) What is the current in the 13-Ω heating element of a 240-V clothes dryer?
(b) How much charge passes through the element in 15 min? (Assume direct current.)
Verified step by step guidance1
Step 1: Use Ohm's Law to calculate the current in the heating element. Ohm's Law is given by \( I = \frac{V}{R} \), where \( I \) is the current, \( V \) is the voltage, and \( R \) is the resistance. Substitute \( V = 240 \, \text{V} \) and \( R = 13 \, \Omega \) into the formula.
Step 2: Once the current \( I \) is determined, calculate the total charge \( Q \) that passes through the element using the relationship \( Q = I \cdot t \), where \( t \) is the time in seconds. Convert the given time of 15 minutes into seconds by multiplying by 60 (\( t = 15 \cdot 60 \)).
Step 3: Substitute the value of \( I \) (calculated in Step 1) and \( t \) (calculated in Step 2) into the formula \( Q = I \cdot t \) to find the total charge.
Step 4: Ensure that the units are consistent throughout the calculations. Voltage is in volts (V), resistance is in ohms (\( \Omega \)), current is in amperes (A), time is in seconds (s), and charge is in coulombs (C).
Step 5: Review the calculations to ensure accuracy and verify that the results align with the physical principles of direct current circuits.
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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 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. It is mathematically expressed as I = V/R. This principle is fundamental for calculating the current in electrical circuits, such as the heating element in the clothes dryer.
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Resistance and Ohm's Law
Electric Charge
Electric charge is a physical property of matter that causes it to experience a force when placed in an electromagnetic field. The unit of charge is the coulomb (C). In the context of the question, the total charge (Q) that passes through the heating element can be calculated using the formula Q = I × t, where I is the current and t is the time in seconds.
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Direct Current (DC)
Direct current (DC) is the unidirectional flow of electric charge, meaning that the electric charge flows in a constant direction. This is in contrast to alternating current (AC), where the flow of charge periodically reverses direction. In the context of the clothes dryer, assuming direct current simplifies the calculations for current and charge over time, as the values remain constant.
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Related Practice
Textbook Question
A 12-V battery causes a current of 0.50 A through a resistor. How many joules of energy does the battery lose in a minute?
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Textbook Question
What voltage will produce 0.25 A of current through a 5400-Ω resistor?
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Textbook Question
Neglect the internal resistance of a battery unless the problem refers to it. Ten 7.0-W Christmas tree lights are connected in series to each other and to a 120-V source. What is the resistance of each bulb?
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Textbook Question
Calculate the terminal voltage for a battery with an internal resistance of 0.900 Ω and an emf of 6.00 V when the battery is connected in series with a 61.0-Ω resistor.
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