Welcome to the Potential Divider!
In our study of Electricity, we’ve seen how batteries provide a fixed voltage. But what if you have a 12V battery and your sensor only needs 3V? You can’t just "ask" the battery for less! This is where the Potential Divider comes in. Think of it as a way to "slice" the total voltage into smaller, usable pieces. By the end of these notes, you’ll be able to design circuits that react to light, heat, and motion.
3.4.5 The Potential Divider Basics
At its simplest, a potential divider is just two or more resistors connected in series across a power supply. Since they are in series, the total Potential Difference (pd) from the battery is shared between them.
How the "Sharing" Works
Imagine a series circuit with two resistors, \(R_1\) and \(R_2\). The battery voltage \(V_{in}\) is shared. The resistor with the highest resistance will always take the biggest share of the voltage.
Analogy: Think of the battery as a pizza. If one person (\(R_1\)) is twice as "hungry" (has more resistance) as the other person (\(R_2\)), they will take a larger slice of the pizza (more voltage)!
The Golden Equation
To find the output voltage (\(V_{out}\)) across a specific resistor (let's say \(R_2\)), we use this formula:
\( V_{out} = \frac{R_2}{R_1 + R_2} \times V_{in} \)
Step-by-Step Breakdown:
1. Total Resistance: Add \(R_1 + R_2\) to find the total resistance in the branch.
2. The Ratio: Divide the resistance you are interested in (\(R_2\)) by the total resistance.
3. The Slice: Multiply that ratio by the input voltage (\(V_{in}\)).
Don't worry if this seems tricky at first! Just remember: The voltage share is proportional to the resistance share. If a resistor has 1/4 of the total resistance, it gets 1/4 of the total voltage.
Quick Review Box:
• High Resistance = Big share of Voltage.
• Low Resistance = Small share of Voltage.
• If \(R_1 = R_2\), then \(V_{out}\) is exactly half of \(V_{in}\).
Constant vs. Variable Potential Dividers
We use potential dividers for two main reasons:
1. Supplying a Constant Voltage: Using two fixed resistors to get a specific voltage that never changes (e.g., getting 5V from a 9V battery).
2. Supplying a Variable Voltage: Replacing one of the resistors with a component whose resistance changes. This allows the \(V_{out}\) to change automatically!
Using Variable Resistors
If we replace \(R_1\) with a variable resistor (rheostat), we can manually turn a knob to change the output voltage. This is exactly how a volume control on an old radio works!
Key Takeaway: By changing the resistance of one part of the divider, you "shift" the voltage share, changing the \(V_{out}\).
Sensors in Potential Dividers
This is where Physics gets really useful. We can use components like LDRs and Thermistors to make circuits that "sense" the world.
1. Light Dependent Resistors (LDR)
An LDR's resistance changes depending on light intensity.
Memory Aid: LURD (Light Up, Resistance Down).
• In the Light: Resistance is Low \( \rightarrow \) Small share of voltage.
• In the Dark: Resistance is High \( \rightarrow \) Big share of voltage.
Example: If you put an LDR in the \(R_2\) position (where \(V_{out}\) is measured), the output voltage will increase as it gets darker. This could be used to turn on a streetlamp!
2. Thermistors (NTC)
In this syllabus, we focus on Negative Temperature Coefficient (NTC) thermistors.
Memory Aid: TURD (Temperature Up, Resistance Down).
• When Hot: Resistance is Low \( \rightarrow \) Small share of voltage.
• When Cold: Resistance is High \( \rightarrow \) Big share of voltage.
Did you know? This is how digital thermometers work. They don't "measure" temperature directly; they measure the changing voltage across a thermistor and convert that number into a temperature reading!
Common Mistake to Avoid:
Students often think that if \(R_1\) increases, its voltage increases and \(R_2\)'s voltage stays the same. This is wrong! Because the total voltage is fixed, if \(R_1\) takes a bigger slice, \(R_2\) must get a smaller slice.
Summary of Sensor Behavior
To decide what happens to \(V_{out}\) in a sensor circuit, follow these steps:
1. Identify what is changing (Light or Temp).
2. Determine if the sensor's resistance is going up or down.
3. See if the sensor is in the \(R_2\) (where we measure \(V_{out}\)) or \(R_1\) position.
4. Use the "Bigger Resistance = Bigger Slice" rule to find the new \(V_{out}\).
Key Takeaway: Potential dividers allow us to turn a change in the environment (light/temp) into a change in voltage that a computer or another circuit can understand.
Final Quick Check
Question: If you want a circuit where the output voltage increases when it gets hotter, where should you put the NTC thermistor?
Answer: When it gets hotter, the thermistor's resistance decreases. To make \(V_{out}\) go up, the other resistor (\(R_2\)) must take a bigger share. Therefore, the thermistor should be in the top position (\(R_1\)). As the thermistor's resistance drops, the fixed resistor at the bottom (\(R_2\)) grabs a larger share of the voltage!