voltage divider with 2 power sources, Vout?

Question

^{simulate this circuit – Schematic created using CircuitLab}

If V2 is NOT present(VB=GND) i can solve it easily using voltage divider formula: I know the steps:

1. I = V1/(R1+R2)
2. Vout = I * R2 =>(i have 'I' from step 1,R2 is known)=> Vout = (V1*R2)/(R1+R2)

Questions:

• A) I would like to request some help on how to solve it when v2 = 3.3 volts is present. Please do not skip steps if you answer it.

  B) Vout is calculated with reference to GND. Right? If yes, that means the voltage drop at R2 equals to Vout = Vout - GND = Vout - 0 = Vout assuming GND as reference point?

  C) Is it correct to say the voltage drop at R2 = Vout - VB? (So in this case i do not take GND as a reference point).

  D) So there are 2 different ways to describe voltage drop? Like case B) and case C).Am i correct?

Answer 1

The key is voltage ACROSS the resistive chain

V = V1 - V2

Then it is a simple voltage divider to work out the voltage across R2

Vr2 = V(R2/(R1+R2))

Finally the output is raised by V2

Vout = Vr2 + V2

Thus. Vout = (V1-V2)(R2/(R1+R2))+V2

Answer 2

Answers:

A) I would like to request some help on how to solve it when v2 = 3.3 volts is present. Please do not skip steps if you answer it.

You need to use the full equation here.

\$V_{OUT} = V_B + (V_A - V_B) * R_2/(R_1 + R_2)\$

which in your example is

\$V_{OUT} = 3.3 + (5 - 3.3) * 667/(200 + 667) = 3.3 + 1.7 * 667 / 867 = 4.61V\$

B) Vout is calculated with reference to GND. Right? If yes, that means the voltage drop at R2 equals to Vout = Vout - GND = Vout - 0 = Vout assuming GND as reference point?

Ok that is a confusing sentence, but essentially correct.

C) Is it correct to say the voltage drop at R2 = Vout - VB? (So in this case i do not take GND as a reference point).

No, the voltage drop ACROSS R2 is Vout-VB.

D) So there are 2 different ways to describe voltage drop? Like case B) and case C).Am i correct?

Since you got off course with C, then this assumption is also incorrect.

Answer 3

The current I is (5 volts - 3.3 volts)/(200 ohms + 667 ohms) = 1.9608 mA.

That current multiplied by R2 (667 ohms) gives you the voltage that Vout is above 3.3 volts i.e. 1.3078 volts hence, Vout = 4.6078 volts.

Answer 4

You could also solve this by producing 2 current equations:

1. I = (VA - VB)/ (R1 + R2)
2. I = (Vout - VB) / (R2)

set them equal... algebra...

Vout = (V1R2 + V2R1)/(R1 + R2)