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For the problem I tried finding the voltage drop then I found R to be 22000R/220

ID: 1275233 • Letter: F

Question

For the problem I tried finding the voltage drop then I found R to be 22000R/22000+R then i pluged it all into R= V/I and got a R of 49.4 ohms but im not sure if thats correct.

Consider the case of a pipe organ that uses an electronic control module to connect the keys to the pipe valves. The key circuit runs on a 24 V DC source. When a key is pressed, a connection is made between the key and a contact completing the circuit. However, the control module input operates at a lower voltage; it wants 4.3 Volts at 400 microamps when the key is pressed. So, a resistor network is used to interface the key contact to the control circuit, and lower the voltage, as shown below. What value of R will give the correct voltage and current when the key is pressed ?

Explanation / Answer

so if 440 uA is going to flow into control then R will have 400 uA less current than 22 kohm

so

24 - 22.0E3*I - 4.3 = 0

I=8.95E-4 A

so current in R is 8.95E-4-400.E-6 = 4.95E-4 A

so V = IR

R = V/I = 4.3/4.95E-4= 8687 ohms or 8.69 kohms