Inside each box there is a resistor and a series switch that can be open or clos
ID: 3202104 • Letter: I
Question
Inside each box there is a resistor and a series switch that can be open or closed. Each switch operates independent of the others, R_1 =44 ohm. is the resistance in the first box and the series switch has probability p_1 = 0.8 of being closed. Similarly, R_2 = 80 ohm, p_2= 0.9, R_3= 20 ohm, p_3 = 0.1. There are 186 volts applied across the above circuit (+ sign at the left end, - sign at the right end) causing current I to flow from left to right. Being a random variable, determine the values that I can take on, the corresponding probabilities.Explanation / Answer
Let us use C or O to denote whether a switch is open or close. So, COO would mean that the first switch is closed whereas the other two are open and so on.
For resistors R1 and R2 in series we know the equivalent resistance is R1+R2 and in parallel it is R1*R2/(R1+R2)
V=186V , p1 = 0.9, p2 = 0.8 and p3 = 0.1 and they are independent
So, the following scenarios are possible
So, I is:
3.1A with p = 0.072
1.5A with p = 0.648
2.91A with p = 0.018
0A with p = 0.262
Scenario Probability Equivalent Resistance Current CCC 0.072(0.9*0.8*0.1) 60 3.1 CCO 0.648 124 1.5 COC 0.018 64 2.91 COO 0.162 inf 0 OCC 0.008 inf 0 OCO 0.072 inf 0 OOC 0.002 inf 0 OOO 0.018 inf 0