Die Spannung U2 am Widerstand R2 soll abhängig von der Schalterstellung sein
Bedingung 1
Bei S=1 wird U2=6V gefordert
Bedingung 2
Bei S=0 soll U2=4V sein
Bedingung 3
Die Summe der Widerstände R1 und R2 ist 10kOhm
Berechne die drei Widerstände R1, R2 und R3
Es sollten wohl 3 Gleichungen geschrieben werden
I.
?..1R=1R1+1R3+R2..?
II.
?..1R=1R2+1R3+R1..?
III.
R1+R2=10kOhm
Solution:
This is a voltage divider circuit. The switch places a third resistor in parallel with (R1) or (R2)
One method of analysis for this circuit is to calculate the resistance values needed to divide 10 volts into a 6v and 4v proportion. The Voltage Divider Formula resolves these values. R2vd=Vs∗R2(R1+R2)|where vd is the voltage drop and Vs is the source voltage.R1vd=Vs∗R1(R1+R2)With a 10 volt source and a 6v drop on R2 and R2 set to 5k ohms, Then 6vd=10vs∗5000(R1+5000)6∗(R1+5000)=50000| divide out voltage and multiply by resistance.6∗R1=20000 →R1=3333.33| in ohms.If (R2) is 5kΩ then (R1) is also 5kΩ because (R1 + R2) = 10kΩ. The switch connects a parallel resistor (R3) to (R1) lowering the resistance to 3333.33 ohms.
Use the Parallel Resistance Formula to find the needed resistance of R3.Rp=(R1+R3)(R1∗R3)|Parallel resistance R3=(−Rp∗R1)(Rp−R1)|Solve for R3 R3=(−3333.33∗5000)(3333.33−5000)R3=(−16666650)(−1666.67)→R3=10000ΩsummaryR1=5kΩR2=5kΩR3=10kΩ
GA