Textbook Question
The current in a wire varies with time according to the relationship . What constant current would transport the same charge in the same time interval?
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Ch 25: Current, Resistance, and EMF
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 25, Problem 23b
What is the resistance of a carbon rod at °C if its resistance is at °C?
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Identify the formula for resistance change with temperature: \( R = R_0 (1 + \alpha \Delta T) \), where \( R \) is the resistance at temperature \( T \), \( R_0 \) is the resistance at the reference temperature, \( \alpha \) is the temperature coefficient of resistance, and \( \Delta T \) is the change in temperature.
Determine the known values: \( R_0 = 0.0160 \; \Omega \) at \( 0.0^\circ C \), \( T = 25.8^\circ C \), and \( \Delta T = 25.8^\circ C - 0.0^\circ C = 25.8^\circ C \).
Look up the temperature coefficient of resistance for carbon, which is typically around \( \alpha = -0.0005 \; ^\circ C^{-1} \).
Substitute the known values into the formula: \( R = 0.0160 \; \Omega (1 + (-0.0005 \; ^\circ C^{-1}) \times 25.8^\circ C) \).
Simplify the expression to find the resistance \( R \) at \( 25.8^\circ C \).
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Resistance
Resistance is a measure of the opposition to the flow of electric current through a conductor. It is influenced by the material's properties, length, and cross-sectional area. The unit of resistance is the ohm (Ω), and it plays a crucial role in determining how much current will flow for a given voltage according to Ohm's Law.
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Resistivity & Resistors in Circuits
Temperature Coefficient of Resistance
The temperature coefficient of resistance indicates how the resistance of a material changes with temperature. For most conductors, resistance increases with temperature. This coefficient is typically expressed in per degree Celsius (°C) and is used to calculate the change in resistance with temperature using the formula R = R0(1 + α(T - T0)), where α is the temperature coefficient.
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Linear Approximation in Resistance Change
Linear approximation assumes that the change in resistance with temperature is linear over a small temperature range. This simplification allows us to use the temperature coefficient of resistance to estimate resistance at a new temperature, given the resistance at a reference temperature. This approach is valid for small temperature changes and materials with a relatively constant coefficient.
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Related Practice
Textbook Question
A copper transmission cable km long and cm in diameter carries a current of A. How much electrical energy is dissipated as thermal energy every hour?
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Textbook Question
A ductile metal wire has resistance . What will be the resistance of this wire in terms of if it is stretched to three times its original length, assuming that the density and resistivity of the material do not change when the wire is stretched? (Hint: The amount of metal does not change, so stretching out the wire will affect its cross-sectional area.)
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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
In household wiring, copper wire mm in diameter is often used. Find the resistance of a -m length of this wire.
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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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