The problem statement : \"Select Values for R1, R2, and R3 in the figure so the
ID: 1832691 • Letter: T
Question
The problem statement :"Select Values for R1, R2, and R3 in the figure so the voltage divider produces the two output voltages shown".
The figure shows an ideal voltage source of 15 V connected in series to the three resistors. R3 is shown to have a voltage drop of 3V, and the combination of R2 and R3 is shown to have a voltage drop of 10 V, thus the voltage over R2 is 7V and the voltage over R1 is 5V. I do not know if I am supposed to come up with arbitrary numbers that are proportional to these values, or if I am supposed to be able to find some exact value for each of the resistors. Because I do not have a current, I do not see how I could come up with any exact numbers. Help is much appreciated.
Explanation / Answer
by voltage divider voltage across R1 Vr1=r1*15/(r2+r3) 5(r2+R3)=15r1 15r1-5r2-5r3=0-------------1 now acorss R2 Vr2=r2*15/(r1+r3) 7(r1+R3)=15r2 7r1-15r2+7r3=0-------------2 similarly acorss R3 Vr3=r3*15/(r1+r2) 3(r1+R2)=15r3 3r1+3r2-15r3=0-------------3 solve 1 2 and 3 we get 15r1-5r2-5r3=0-------------1 7r1-15r2+7r3=0-------------2 3r1+3r2-15r3=0-------------3 r2=3.5r3 r1=91/14r3 since above equation have infiinite no of solution hence assume any value of r3 ,you will get value of r1 and r2 the only uniqe solution of above system is 0.0.0 which is not possible in our case ..hence there are infinte value which will satiesfy our case BEST OF LUCK
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