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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
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Non è quello che usi tu?Cambia libro di testo
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Young & Freedman Calc 14th EditionCh 25: Current, Resistance, and EMFProblema 23b
Young & Freedman Calc 14th EditionCh 25: Current, Resistance, and EMFProblema 23bCapitolo 25, Problema 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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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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Percorso guidato
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.
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Percorso guidato
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.
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07:31Linear Thermal Expansion
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