Question:
"The resistance R3 in the diagram is the equivalent resistance of a pressure transducer. This resistance is specified to be 200Ω ± 5%. The voltage source is a 12V ± 1% source capable of supplying 5W. Design this circuit, using 5%, 1/8W resistors for R1 and R2, so that the voltage across R3 is Vo=4V±10%."
Attempt:
I'm ignoring the error margins for the moment and just working with the specified values.
The voltage drop accross R2 must be 8V, therefore I*R2=8. Each resistor can only dissipate 1/8W, so
\(\frac{8^{2}}{R_{2}}\leq\frac{1}{8}\)
\(R_{2}\geq512\).
The equivalent resistance of the circuit is
\(R_{T}=R_{2}+\frac{R_{1}R_{3}}{R_{1}+R_{3}} = R_{2} + \frac{200R_{1}}{R_{1}+200}\).
Therefore
\(12=IR_{T}\)
\(12=\frac{8}{R_{2}}(R_{2}+\frac{200R_{1}}{R_{1}+200})\)
\(12R_{2}=8R_{2}+\frac{1600R_{1}}{R_{1}+200}\)
\(R_{2}=\frac{400R_{1}}{R_{1}+200}\)
\(R_{1}+200=\frac{400R_{1}}{R_{2}}\).
So if R2>512Ω (required by the power restrictions), you are bound to require a negative value for R1. Am I doing something silly here, or does the question not work?
Thanks for any help!
Jon.
"The resistance R3 in the diagram is the equivalent resistance of a pressure transducer. This resistance is specified to be 200Ω ± 5%. The voltage source is a 12V ± 1% source capable of supplying 5W. Design this circuit, using 5%, 1/8W resistors for R1 and R2, so that the voltage across R3 is Vo=4V±10%."
Attempt:
I'm ignoring the error margins for the moment and just working with the specified values.
The voltage drop accross R2 must be 8V, therefore I*R2=8. Each resistor can only dissipate 1/8W, so
\(\frac{8^{2}}{R_{2}}\leq\frac{1}{8}\)
\(R_{2}\geq512\).
The equivalent resistance of the circuit is
\(R_{T}=R_{2}+\frac{R_{1}R_{3}}{R_{1}+R_{3}} = R_{2} + \frac{200R_{1}}{R_{1}+200}\).
Therefore
\(12=IR_{T}\)
\(12=\frac{8}{R_{2}}(R_{2}+\frac{200R_{1}}{R_{1}+200})\)
\(12R_{2}=8R_{2}+\frac{1600R_{1}}{R_{1}+200}\)
\(R_{2}=\frac{400R_{1}}{R_{1}+200}\)
\(R_{1}+200=\frac{400R_{1}}{R_{2}}\).
So if R2>512Ω (required by the power restrictions), you are bound to require a negative value for R1. Am I doing something silly here, or does the question not work?
Thanks for any help!
Jon.
Last edited: