Chapter 26, Problem 26P

(III) You are designing a wire resistance heater to heat an enclosed volume of gas. For the apparatus to function properly, this heater must transfer heat to the gas at a very constant rate. While in operation, the resistance of the heater will always be close to the value R = R₀, but may fluctuate slightly causing its resistance to vary a small amount ∆R (≪ R₀). To maintain the heater at constant power, you design the circuit shown in Fig. 26–44, which includes two resistors, each of resistance r. Determine the value for r so that the heater power will remain constant even if its resistance R fluctuates by a small amount. [Hint: If ∆R ≪ R₀, then $\Delta P\approx \Delta R{\frac{dP}{dR}|}_{R-R_0}$.]