Introduction:
The resistance of a carbon resistor can be affected by temperature. This relationship can be expressed using the equation a b log R = √(log R/T), where R is the resistance and T is the temperature.

Calculation:
To calculate the temperature, we need to rearrange the equation and isolate T.

1. Start by squaring both sides of the equation to eliminate the square root:
(a b log R)^2 = log R/T

2. Expand the left side of the equation:
(a b)^2 (log R)^2 = log R/T

3. Multiply both sides by T to eliminate the fraction:
T (a b)^2 (log R)^2 = log R

4. Divide both sides by (a b)^2 (log R)^2:
T = log R / [(a b)^2 (log R)^2]

Explanation:
The equation T = log R / [(a b)^2 (log R)^2] allows us to calculate the temperature T using the resistance R and the constants a and b.

The relationship between resistance and temperature in a carbon resistor is complex and can be affected by factors such as the composition of the resistor and the temperature coefficient of resistance. The equation provided represents a simplified relationship that may be applicable under certain conditions.

It is important to note that this equation assumes a linear relationship between resistance and temperature, which may not hold true in all cases. Additionally, the equation does not take into account other factors such as self-heating of the resistor or the effect of temperature on the resistor's power rating.

Overall, while the provided equation can provide an estimate of the temperature based on resistance, it is essential to consider the specific characteristics of the resistor and the conditions under which it is operating for accurate results.