1. The Voltage Divider Key to Big Ideas
Practical Implementation of Circuits
Theory-Simulation-Experiment (Compare & Contrast)
Direct Uses (Finding ZIN or ZOUT, Voltage Standard, Model for Filters and Other Types of Circuits …)
Fundamentals (Ohm’s Law, Linear Systems …)

2. The Voltage Divider
Note that there are several points in this video where you are encouraged to pause and think about a question. To do this you will have to press Pause (lower left on YouTube window) and then Play when you are ready to proceed. You will be reminded of this with the following symbol:
12 November 2018

3. The Voltage Divider
Before Addressing the Voltage Divider, Recall Ohm’s Law
From Wikipedia
Plot Current I vs Voltage V
Slope is
Outcomes
Large Resistor: Small Current
Small Resistor: Large Current
(Same Voltage)
12 November 2018

4. The Voltage Divider
12 November 2018

5. The Voltage Divider
12 November 2018

6. The Voltage Divider Where Does the Formula Come From?
For the derivation, simplify the circuit by combining the two resistors into one with value R1+R2. Then find the current by dividing Vin by (R1+R2).
12 November 2018

7. The Voltage Divider Where Does the Formula Come From?
Next determine the output voltage Vout by multiplying the current determined in the last slide by the resistance R2. The result is the voltage divider formula.
12 November 2018

8. The Voltage Divider Can the Formula Be Used in Other Ways? Knowns
Unknowns
Vin, R1, R2
Vout
Give the students a clue by pointing out that there are 4 parameters in the voltage divider equation. Then give them a chance to think about this. Reveal the answer after they think about it for a few minutes. I ask the students to pause here on the video.
If we can measure any three, we can determine the 4th
12 November 2018

9. The Voltage Divider Can the Formula Be Used in Other Ways? Knowns
Unknowns
Vin, R1, R2
Vout
R1, R2, Vout
Vin
Vin, R2, Vout R1
Vin, R1, Vout R2
Two unknowns or more require multiple measurements by changing R1, R2 or both. Usually only one needs to be changed. One can also change Vin if there are different power supplies. The key is that N unknowns require N equations so N experiments with somewhat different parameters.
Measurement errors, noise, parameters that vary with time (age) like battery voltage are reasons to make more than one set of measurements. At least one can average out errors or better identify errors that way.
What happens if we have 2 unknowns or even more? What experiment can we do to figure out all four parameters?
Are there other reasons to make more than one set of measurements?
12 November 2018

10. The Voltage Divider Finding Unknown Resistor Battery as Source:
Unknowns are Vin and R1 (Vbat varies with time so not known exactly)
Measure Vout with no R2 connected (open circuit load)
Vin = Vbat = Vout (open circuit)
Connect R2 with value similar to guess for R1
Determine R1 from Voltage Divider Equation
In this slide and the next, consider a case where R1>>R2 or vice versa. Also check to see what happens when R1 = R2. Sanity checks are relatively simple.
Does this answer make sense?
12 November 2018

11. The Voltage Divider Finding Unknown Resistor Battery as Source:
Unknowns are R2 and Vbat
Use R1 with a value similar to your guess for R2
Measure Vout with no R2 connected (open circuit load).
Connect unknown resistor R2
Use Voltage Divider formula to find R2
Does this answer make sense?
12 November 2018

12. The Voltage Divider
Many devices have an unknown resistance until you measure it. For smart systems run by Arduinos, it is necessary to know what the output and input impedances of the Arduino are.
Resistive sensors should be really obvious. Their resistance changes with whatever they are sensitive to. Photocells have a dark resistance of around 1Meg while in bright light the resistance can be about 1k. We have to measure the resistance to know what the light level is.
Can find Input Impedance for Most Black Boxes Using this Method
Also Useful for Resistive Sensors
12 November 2018

13. The Voltage Divider Example of Resistive Sensors
Photocell (LDR) – Resistance changes with light level
Strain Gauge – Resistance changes slightly when stretched or compressed
Force Sensor (FSR) – Resistance changes with pressure
Strain Gauge – wires stretched become longer and thinner – both increase R
Photocell – semiconductor charge carriers are created by photon impact
DIY Strain Gauge
12 November 2018

14. The Voltage Divider R2 is Resistive Sensor
This slide just points out the key reason for us to learn this – sensors.
R2 is Resistive Sensor
12 November 2018

15. The Voltage Divider
To Be Continued …
12 November 2018