+514 
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.
\(?..{1 \over R} ={1 \over R_1} + {1 \over R_3}+R_2..?\)
II.
\(?..{1 \over R} ={1 \over R_2} + {1 \over R_3}+R_1..?\)
III.
R1+R2=10kOhm
+2440 Solution:
This is a voltage divider circuit. The switch places a third resistor in parallel with (R1) or (R2)
\(\text {One method of analysis for this circuit is to calculate the resistance values needed to divide 10 volts into a 6v and 4v proportion. }\\ \text {The Voltage Divider Formula resolves these values. }\\ R2_{vd} = Vs * \frac {R2}{(R1+R2)} | \text {where vd is the voltage drop and Vs is the source voltage.} \\ R1_{vd} = Vs * \frac{R1}{(R1+R2)} \\ \text {With a 10 volt source and a 6v drop on R2 and R2 set to 5k ohms, }\\ \text {Then } 6_{vd} = 10_{vs} * \frac {5000}{(R1 +5000) }\\ 6 * (R1 + 5000) =50000 \; \;| \text { divide out voltage and multiply by resistance.}\\ 6*R1 = 20000 \ \rightarrow R1= 3333.33 \;\; | \text { in ohms.}\\ \text {If (R2) is 5k$\Omega$ then (R1) is also 5k$\Omega$ because (R1 + R2) = 10k$\Omega$. }\\ \text {The switch connects a parallel resistor (R3) to (R1) lowering the resistance to 3333.33 ohms. }\\ \)
\(\\ \text {Use the Parallel Resistance Formula to find the needed resistance of R3.}\\ Rp = \frac {(R1 + R3)} {(R1 * R3)} \;\; |\text {Parallel resistance }\\ R3 = \frac { (-Rp * R1)}{(Rp - R1)} \;\;\;\;\; |\text {Solve for R3 }\\ R3 = \frac {(-3333.33 * 5000)}{(3333.33 - 5000)}\\ R3 = \frac {(-16666650)} {(-1666.67)} \rightarrow R3 = 10000 \Omega \\ \text {summary}\\ R1 = 5k \Omega \\ R2 = 5k \Omega \\ R3 = 10k \Omega \\ \)
GA
