solution2626 - Ch 26 26(III You are designing a wire...

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Ch. 26 26. (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 0 , RR but may fluctuate slightly causing its resistance to vary a small amount R D   0 R. 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 0 , D then 0 dP P R . dR DD < 0 ] [Solution] The goal is to determine r so that 0 0. R dP dR This ensures that R produce very little change in , R P since . R R dP PR dR The power delivered to the heater can be found by 2 heater heater , P V R and so we need to determine the voltage across the heater.
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