A resistor is to have a constant resistance of 30(ohm), independent of temperature. For this, an aluminum resistor with resistance R1 at 0(Celsius) is used in series with a carbon resistor with resistance R2 at 0(Celsius). Evaluate R1 and R2,
Since you did not give a unit to the temperature coefficients, I suppose they are in unit of C^-1 It is required that: R01 + R02 = 30 ohms --------------------- (1) Suppose the temperature rises by T degrees C change of resistance of R01 = (R01) x (3.9x10^-3) x T change of resistance of R02 = (R02) x (-0.5x10^-3) x T For the total resistance to be kept at 30 ohms, we need to have, change of resistance of R01 + change of resistance of R02 = 0 i.e. [(R01) x (3.9x10^-3) x T] + [ (R02) x (-0.5x10^-3) x T] = 0 [(R01) x (3.9x10^-3) = (R02) x (0.5x10^-3) (R02) = (R01) x [3.9x10^-3/0.5x10^-3] = 7.8(R01) Substitute into equation (1) R01 + 7.8(R01) = 30 hence, R01 = 3.409 ohms and R02 = 7.8 x 3.409 ohms = 26.59 ohms
The above reply by Henry is USELESS
Henry's reply sucks
To evaluate R1 and R2, we need to use the temperature coefficient of resistance (TCR) for aluminum and carbon. The TCR represents the change in resistance for one degree Celsius change in temperature.
Let's assume the TCR for aluminum is α1 (in ohms per degree Celsius) and the TCR for carbon is α2 (in ohms per degree Celsius).
Since the resistance of the aluminum resistor is constant at 30 ohms independent of temperature, we can write:
R1 = 30 ohms
Now, let's consider the carbon resistor. We need to find its resistance R2 at 0 degrees Celsius.
To find R2, we can use the formula for the resistance-temperature relationship:
R2 = R2_0 (1 + α2 * ΔT)
Where:
R2_0 - Resistance of the carbon resistor at 0 degrees Celsius (unknown)
α2 - Temperature coefficient of resistance of carbon (unknown)
ΔT - Change in temperature in degrees Celsius (0 - 0 = 0)
Since we want R2_0 to be such that the overall resistance is constant at 30 ohms, we can set up the equation:
R1 + R2_0 = R_total
30 ohms + R2_0 = 30 ohms
Simplifying, we find:
R2_0 = 30 ohms - R1
R2_0 = 30 ohms - 30 ohms
R2_0 = 0 ohms
Therefore, for the overall resistance to be constant at 30 ohms independent of temperature, R1 should be 30 ohms and R2 should be 0 ohms.
However, please note that in reality, it is not possible for a resistor to have zero resistance. This example assumes ideal resistors for the purpose of demonstration.
R1 + R2 = 30 Ohms.
The temperature coefficient of R1 and R2 must be equal and opposite.
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