# Voltage division question

## 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 whats wrong?

#### Attachments

• Voltage division.png
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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.

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 travelled through the same line as v and onwards.

berkeman
Mentor

## 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 whats 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.

... 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.

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