A pair of resistors R 1 and R 2 share the wattage of W watts totally dissipated by them in the circu

A pair of resistors R1 and R2 share the wattage of W watts totally dissipated by them in the circuit of Figure. III-A Determine the currents I1 and I2 in terms of R1, R2, and W. (Ans: I1 = (W/Rp)1/2 × [R2/(R1+R2)] A; I2 = ?) – Hint: Use current division theorem Suppose R1-30 and R2-30, denote the values of R1 and R2 respectively at room temperature 30oC. These elements are made of two different conducting materials of conductivities, s1 and s2 siemen/m (respectively) at room temperature (30oC); and, they are of identical geometry (of length L meter and cross sectional area A m2). The temperature coefficients of resistivity of the heating elements, R1 and R2 are a1/oC and a2 /oC respectively. Determine the values of the conductance, G1, and G2 at 100oC.

[Ans: G1-100 = G1-30/(1+70a1), unit ?; G2-100 = ?]

In Fig. 3, the current (I1) through R1 is set to control a current-controlled voltage- operated switch (trip-switch); and Vs = bI1. Suppose the switch/trip operates when Vs = VThreshold. Determine the corresponding threshold temperature (TThreshold) in terms of {V, VThreshold, b, s1, a1 and A/L}, at which the switch will trip.

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FIGURE III-A I R2 I2 + +

 

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