Can anyone help with this?

Nov 2019
1
0
England
For the system below, a potentiometer of 1kΩ is used as a voltage divider. Later on, a load which has a 10kΩ resistance is added.
a. In the absence of the 10kΩ load, what are the values of R1 and R2 to establish 3V across R2 ?
b. Determine the values of R1 and R2 to establish VRL = 3V when the load is applied.


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Jan 2019
51
37
(a) 9V across $R_1$ and 3V across $R_2 \implies R_1 = 3R_2 \implies 4R_2 = 1 \, k\Omega$

(b) Combining the parallel resistors, $R_{eff} = \dfrac{R_2 \cdot R_L}{R_2 + R_L}$

Same reasoning as part (a) yields $R_1 = 3R_{eff} = \dfrac{3 \cdot R_2 \cdot R_L}{R_2 + R_L}$

Also know $R_1 + R_2 = 1 \, k\Omega \implies R_1 = \color{red}{1 \, k\Omega - R_2 = \dfrac{3 \cdot R_2 \cdot R_L}{R_2 + R_L}}$.

Solve the last equation for $\color{red}R_2$, and subsequently $R_1$.
 
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