교과서 질문
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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Ch 25: Current, Resistance, and EMF
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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TOC.tableOfContents
- 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
25장, 문제 23b
What is the resistance of a carbon rod at °C if its resistance is at °C?
검증된 단계별 안내1
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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주요 개념
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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.
추천 영상:
가이드 코스
05:25
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.
추천 영상:
가이드 코스
04:54Introduction To Temperature Scales
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.
추천 영상:
가이드 코스
07:31Linear Thermal Expansion
관련 실천
교과서 질문
A hollow aluminum cylinder is m long and has an inner radius of cm and an outer radius of cm. Treat each surface (inner, outer, and the two end faces) as an equipotential surface. At room temperature, what will an ohmmeter read if it is connected between (a) the opposite faces and (b) the inner and outer surfaces?
1596
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교과서 질문
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.)
2322
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교과서 질문
An idealized ammeter is connected to a battery as shown in Fig. E. Find the reading of the ammeter.
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교과서 질문
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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교과서 질문
An idealized ammeter is connected to a battery as shown in Fig. E. Find the current through the - resistor.
2106
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