Understanding Voltage Division in Circuits: A Superposition Approach

[TsAmE]

Homework Statement

Calculate v (refer to attachment).

Homework Equations

Voltage division: Vout = Vin x R2 / R1 + R2

The Attempt at a Solution

V1 = V1 x R2 / R1 + R2
= 15 x 5 / 10 + 5
= 5V

V2 = V2 x R4 / R3 + R4
= 5 x 2 / 10 + 2
= 0.83V

V = 5 + 0.83
= 5.83V

But my answer is wrong. Could someone please tell me what's wrong?

 

[xcvxcvvc]

Have you tried nodal analysis, or are you supposed to use "voltage division" to solve it for academic perfection of the technique?

$$I_1 + I_2 + I_3 + I_4 = 0$$
where I_1 through i_4 refer to the four currents going through the four resistors. Every single current can be written in terms of the voltage across the resistor and the resistance.

 

[TsAmE]

I am supposed to use voltage division.

In connection with how the current flows (if this was part of an actual circuit), would it be like this:

*The current from the +15V supply (I1) spilts into 2 currents: the one flows from the midpoint to Earth (I2), and the other one flows to the right of the mid point (I3). I1 = I2 + I3.
*The current from the +5V supply (I4) spilts into 2 currents: the one flows from the midpoint to Earth (I5), and the other one flows to the right of midpoint (I6). I4 = I5 + I6.
*I3 would have joined with I6 then traveled through the same line as v and onwards.

 

[berkeman]

Homework Statement

Calculate v (refer to attachment).

Homework Equations

Voltage division: Vout = Vin x R2 / R1 + R2

The Attempt at a Solution

V1 = V1 x R2 / R1 + R2
= 15 x 5 / 10 + 5
= 5V

V2 = V2 x R4 / R3 + R4
= 5 x 2 / 10 + 2
= 0.83V

V = 5 + 0.83
= 5.83V

But my answer is wrong. Could someone please tell me what's wrong?

I don't know how to use "voltage division" when you have multiple inputs like that. Doesn't make sense to me... Maybe there's some superposition trick, but I'm not seeing it.

 

[Yaz Li]

... Maybe there's some superposition trick, ...

I think you are right. Superposition with voltage division can solve this.

1) Contribution of +15V:

V=(2k||10k||5k)*15/(10k+2k||10k||5k)=1.25k*15/(10k+1.25k)=1.667V

2) Contribution of -15V:

V=(2k||10k||10k)*(-15V)/(5k+2k||10k||10k)=1.429k*(-15)/(6.429)=-3.333V

3) Contribution of 5V:

V=(2k||10k||5k)*5V/(10k+2k||10k||5k)=1.25k*5V/(10k+1.25k)=0.556V

Superposition:
V=1.667-3.333+0.556=-1.11V

I have a http://www.solved-problems.com/tag/voltage-divider/". I need to add one similar to this.