Final answer:
To create a voltage divider for a 4-V output from 10-V supply while limiting current through each resistor to less than 1 mA, suitable resistor values could be R1 = 15 kΩ and R2 = 10 kΩ. These values maintain the required voltage division ratio and keep the total resistance above 10 kΩ, thus restricting current as requested.
Step-by-step explanation:
In order to design a voltage divider that takes a 10-V supply and creates a 4-V output while keeping the current through each resistor less than 1mA, you can use the following approach:
Firstly, you select resistor values that will produce the required voltage output. According to the voltage divider rule,
Vout = Vin(R2 / (R1 + R2)), where R1 and R2 are the resistors in series. To achieve a 4-V output from a 10-V input, you could choose R1 and R2 such that R2/(R1 + R2) = 4/10 = 0.4.
Keeping current considerations in mind, since the desired current is less than 1mA, select resistor values that, when combined with the voltage, result in a current less than 1mA. Using Ohm's law (
I = V/R), the minimum combined resistance should be R = V/I = 10V/1mA = 10,000 Ω (10 kΩ).
By satisfying both the voltage ratio and current requirements, suitable values for R1 and R2 would be, for example, R1 = 15 kΩ and R2 = 10 kΩ. This would give a division ratio of 10 kΩ/(15 kΩ + 10 kΩ) = 0.4, thereby producing the 4V output, and keeping the current below 1mA since the total resistance exceeds 10 kΩ.