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The resistance R' of a particular carbon resistor obeys the equation Squareroot log R'/T = a b log R', where a = -1.16 and b = 0.675. In a liquid helium cryostat, the resistance is found to be exactly 1000 Ohm (ohms). What is the temperature?
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The resistance R' of a particular carbon resistor obeys the equation S...
Resistance and Temperature Relationship
The resistance of a material is known to vary with temperature. This relationship is given by the equation:
Squareroot log R'/T = a b log R'
where R' is the resistance, T is the temperature, and a and b are constants.
Given Values:
- a = -1.16
- b = 0.675
- Resistance (R') = 1000 Ohm
Finding the Temperature
To find the temperature (T) corresponding to the given resistance (R' = 1000 Ohm), we can rearrange the equation and solve for T.
Squareroot log R'/T = a b log R'
Taking the square of both sides:
log R'/T = (a b log R')²
Exponentiating both sides:
e^(log R'/T) = e^((a b log R')²)
Simplifying the right side:
R'/T = e^(a² + 2ab log R' + b² (log R')²)
Rearranging the equation:
T = R' / e^(a² + 2ab log R' + b² (log R')²)
Substituting the given resistance (R' = 1000 Ohm) into the equation, we can calculate the temperature (T).
T = 1000 / e^(a² + 2ab log 1000 + b² (log 1000)²)
Calculating the Temperature
Using the given values of a, b, and R', we can calculate the temperature using the above equation.
T = 1000 / e^((-1.16)² + 2(-1.16)(0.675) log 1000 + (0.675)² (log 1000)²)
Solving this equation, we find the temperature T.
The resistance of a material is known to vary with temperature. This relationship is given by the equation:
Squareroot log R'/T = a b log R'
where R' is the resistance, T is the temperature, and a and b are constants.
Given Values:
- a = -1.16
- b = 0.675
- Resistance (R') = 1000 Ohm
Finding the Temperature
To find the temperature (T) corresponding to the given resistance (R' = 1000 Ohm), we can rearrange the equation and solve for T.
Squareroot log R'/T = a b log R'
Taking the square of both sides:
log R'/T = (a b log R')²
Exponentiating both sides:
e^(log R'/T) = e^((a b log R')²)
Simplifying the right side:
R'/T = e^(a² + 2ab log R' + b² (log R')²)
Rearranging the equation:
T = R' / e^(a² + 2ab log R' + b² (log R')²)
Substituting the given resistance (R' = 1000 Ohm) into the equation, we can calculate the temperature (T).
T = 1000 / e^(a² + 2ab log 1000 + b² (log 1000)²)
Calculating the Temperature
Using the given values of a, b, and R', we can calculate the temperature using the above equation.
T = 1000 / e^((-1.16)² + 2(-1.16)(0.675) log 1000 + (0.675)² (log 1000)²)
Solving this equation, we find the temperature T.
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The resistance R' of a particular carbon resistor obeys the equation Squareroot log R'/T = a b log R', where a = -1.16 and b = 0.675. In a liquid helium cryostat, the resistance is found to be exactly 1000 Ohm (ohms). What is the temperature?
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The resistance R' of a particular carbon resistor obeys the equation Squareroot log R'/T = a b log R', where a = -1.16 and b = 0.675. In a liquid helium cryostat, the resistance is found to be exactly 1000 Ohm (ohms). What is the temperature? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The resistance R' of a particular carbon resistor obeys the equation Squareroot log R'/T = a b log R', where a = -1.16 and b = 0.675. In a liquid helium cryostat, the resistance is found to be exactly 1000 Ohm (ohms). What is the temperature? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The resistance R' of a particular carbon resistor obeys the equation Squareroot log R'/T = a b log R', where a = -1.16 and b = 0.675. In a liquid helium cryostat, the resistance is found to be exactly 1000 Ohm (ohms). What is the temperature?.
The resistance R' of a particular carbon resistor obeys the equation Squareroot log R'/T = a b log R', where a = -1.16 and b = 0.675. In a liquid helium cryostat, the resistance is found to be exactly 1000 Ohm (ohms). What is the temperature? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about The resistance R' of a particular carbon resistor obeys the equation Squareroot log R'/T = a b log R', where a = -1.16 and b = 0.675. In a liquid helium cryostat, the resistance is found to be exactly 1000 Ohm (ohms). What is the temperature? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The resistance R' of a particular carbon resistor obeys the equation Squareroot log R'/T = a b log R', where a = -1.16 and b = 0.675. In a liquid helium cryostat, the resistance is found to be exactly 1000 Ohm (ohms). What is the temperature?.
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