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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.
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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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