Please show all steps and state intuition behind this and other type problems si

Question

Please show all steps and state intuition behind this and other type problems similar. Thank you,

1. Analysis: The circuit diagram is shown to the right. Both batteries are 5 V. Find the values of R1 and R2 that will give an output voltage of Vout = 2.5 V, and a supply current of 1 mA. Then find the values that will give the correct output voltage with a supply current of 5 mA.

Prove that you can set R1 + R2 to get the desired current, and then set R2/R1 to get the desired voltage.

Here is the circuit diagram: Please advise on it as well. It's here:

https://3395680149491214243-a-eng-ucsd-edu-s-sites.googlegroups.com/a/eng.ucsd.edu/ece-35-spring-2012/lab-files/Lab_1_Updated?attachauth=ANoY7cq6IRaipJX8BB2nNsJUit6JZIsgiaZuyzx9HWYrlcK335JOPVJgLCbn_DklIHcnsvhFADY_WtpSyVdtfuO6En6alIzjk48xIQ25jZhQp6fNz7gOk95DQmxZiLrwejLbd-wtn8ThN2lEejyJ63rMWKwIzDGKWHOwlIe2Ree6XNY2d_OWnniRKMDVvosBhGlTzx7RMDkZHdW0OYVHDWCsdyynrwyNjQ%3D%3D&attredirects=0

Explanation / Answer

Both the batteries are connected in series so there voltages will add up and we will get a voltage of 10V . in order to get 2.5V drop across the output resistor R1/R2=3 i.e R1 should be 3 times greater than R2. e.g. if R2 is taken to be 2.5 kilo ohms then R1 should be 7.5 kilo ohms and the equivalent resistance will be Req=10kohms I=V/Req=10/10k = 1mA and VR2= I*R2= 2.5V If the current is to become 5mA then Req=V/I=10/5m=2 Kohms as R1=3R2 R2=.5 kohms and R1=1.5 k ohms VR2=I*R2 = .5K *5m=2.5V As the current in the circuit is given by I=V/Req and Req=R1+R2 so I=V/(R1+R2) as the supply voltage remains constant so I is inversely proportional to (R1+R2), hence by controlling these we can change our current. By intuition we can observe that voltage across R2 depends upon its weightage with respect of R1. e.g if R1 is 2 times R2 then there will be double the voltage across R1 than R2. so we can change the output voltage by changing the ratio of both the resistances i.e R1/R2

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