The resistances of commercially-available discrete resistors are restricted to p

Question

The resistances of commercially-available discrete resistors are restricted to particular sets. For example, the available values of resistors with 10% tolerance are selections from the E12 set multiplied by a power of ten from 10^0 through 10^5. The E12 set is E12 = {10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82} Thus, you can buy 10% resistors with a nominal resistance of 330 Ohm or 33k Ohm, but not 350 Ohm. The "tolerance" means that if you buy a 10% 390 Ohm resistor you can be sure that its resistance is between 351 Ohm and 429Ohm. In this problem we need to choose 10% resistors to make a voltage divider that meets a given specification We are given an input voltage Vin = 80.0V, and we need to provide an open-circuit output voltage of Vout 20.0V. An additional requirement is that the Theventn resistance as seen from the output terminals is between 10k Ohm and 30k Ohm. Assume first that the resistors have their nominal resistance. Come up vwth resistors R1 and R2 such that the division ratio Vout/Vin is within 10% of the requirement. Of course, the resistances you chose are just nominal. Given that they are only guaranteed to have resistances within 10% of the nominal value, what is the largest and smallest value that Vout may have? Enter your values here R1 (in Ohms): R2 (in Ohms): vmax ( in Volts): Vmin (in volts):

Explanation / Answer

Vin = 80V Vout(open) ˜ 20V
Using voltage divider rule Vout = Vin R2 / (R1 + R2)
20 = 80  R2 / (R1 + R2) R2 / (R1 + R2) = 0.25 ---------------- (1) The Thevenin's resistance Rth =  R1 R2 / (R1 + R2)   Given Rth is between 10k and 30k Let Rth = 20k 20000 =  R1 R2 / (R1 + R2) ---------- (2) From (1) and (2) 20000 = 0.25R1 R1 = 80k
R2 / (80000 + R2 ) = 0.25 4R2 = 80000 + R2 3R2 = 80000 R2 = 26.66k
The resistor values from calculations are R1 = 80k and R2 = 26.66k
To select the commercially available resistors with 10% tolerance R1 = 82k and R2 = 27k
The resistance R1 can be between 90.2k and 73.8k The resistance R2 can be between 29.7k and 24.3k
With R1 = 90.2k and R2 = 29.7k, Vout = (80)(29700)/(29700+90200) = 19.8V
With R1 = 90.2k and R2 = 24.3k, Vout = (80)(24300)/(24300+90200) = 17V
With R1 = 73.8k and R2 = 29.7k, Vout = (80)(29700)/(29700+73800) = 29V
With R1 = 73.8k and R2 = 24.3k, Vout = (80)(24300)/(24300+73800) = 19.8V
Vout(max) = 29V Vout(min) = 17V


R1 = 80k
R2 / (80000 + R2 ) = 0.25 4R2 = 80000 + R2 3R2 = 80000 R2 = 26.66k
The resistor values from calculations are R1 = 80k and R2 = 26.66k
To select the commercially available resistors with 10% tolerance R1 = 82k and R2 = 27k
The resistance R1 can be between 90.2k and 73.8k The resistance R2 can be between 29.7k and 24.3k
With R1 = 90.2k and R2 = 29.7k, Vout = (80)(29700)/(29700+90200) = 19.8V
With R1 = 90.2k and R2 = 24.3k, Vout = (80)(24300)/(24300+90200) = 17V
With R1 = 73.8k and R2 = 29.7k, Vout = (80)(29700)/(29700+73800) = 29V
With R1 = 73.8k and R2 = 24.3k, Vout = (80)(24300)/(24300+73800) = 19.8V
Vout(max) = 29V Vout(min) = 17V


3R2 = 80000 R2 = 26.66k
The resistor values from calculations are R1 = 80k and R2 = 26.66k
To select the commercially available resistors with 10% tolerance R1 = 82k and R2 = 27k
The resistance R1 can be between 90.2k and 73.8k The resistance R2 can be between 29.7k and 24.3k
With R1 = 90.2k and R2 = 29.7k, Vout = (80)(29700)/(29700+90200) = 19.8V
With R1 = 90.2k and R2 = 24.3k, Vout = (80)(24300)/(24300+90200) = 17V
With R1 = 73.8k and R2 = 29.7k, Vout = (80)(29700)/(29700+73800) = 29V
With R1 = 73.8k and R2 = 24.3k, Vout = (80)(24300)/(24300+73800) = 19.8V
Vout(max) = 29V Vout(min) = 17V

With R1 = 90.2k and R2 = 24.3k, Vout = (80)(24300)/(24300+90200) = 17V
With R1 = 73.8k and R2 = 29.7k, Vout = (80)(29700)/(29700+73800) = 29V
With R1 = 73.8k and R2 = 24.3k, Vout = (80)(24300)/(24300+73800) = 19.8V
Vout(max) = 29V Vout(min) = 17V
With R1 = 73.8k and R2 = 29.7k, Vout = (80)(29700)/(29700+73800) = 29V
With R1 = 73.8k and R2 = 24.3k, Vout = (80)(24300)/(24300+73800) = 19.8V With R1 = 73.8k and R2 = 24.3k, Vout = (80)(24300)/(24300+73800) = 19.8V
Vout(max) = 29V Vout(min) = 17V

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