A type- \(\mathrm{K}\) thermocouple produces a voltage that is proportional to temperature. The characteristic of a type-K thermocouple is shown in Figure P2-67. (a). In an application, this transducer is used to detect when the temperature reaches \(1250^{\circ} \mathrm{C}\) and then to cause a safety shutoff to trip and stop an operation. The safety shutoff can be modeled by a \(5-\mathrm{k} \Omega\) input resistance, while the transducer can be modeled by a variable voltage source, \(v(\mathrm{~T})\), in series with a resistance of \(33 \Omega\) to account for the transducer's wires and internal resistance as shown in Figure P2-67 (b). The safety shutoff will trip when exactly \(10 \mathrm{mV}\) is applied. Select an appropriate resistance \(R\) that will cause the safety shutoff to trip at exactly \(1250^{\circ} \mathrm{C}\).

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Thermocouple output voltage (mV) 80 70 60 50 40 30 20 10 0 v(T) E 0 500 1000 1000 Temperature () 33 (2 www - thermocouple P K (b) Ris (a) -C 1500 2000 2500 5 km2 Safety shutoff