Upon successful completion of this module, the student will be able to:
Explain the principle of a voltage divider and apply the Voltage Divider Rule as a shortcut for circuit analysis.
Explain the principle of a current divider and apply the Current Divider Rule as a shortcut for circuit analysis.
Differentiate between a potentiometer and a rheostat based on their construction, schematic symbols, and applications.
Analyze and troubleshoot circuits containing potentiometers, such as automotive sensor circuits.
Analyze and troubleshoot circuits containing rheostats, such as motor speed control circuits.
So far, we've dealt with circuits where everything is fixed. But the real world isn’t static. The most interesting and powerful systems need to be adjustable. They need to sense movement, send variable signals, and control the flow of power in real-time.
This is where you level up from a circuit analyst to a circuit controller. We'll cover the fundamental building blocks of control: Voltage Dividers, Current Dividers, and their physical forms, the potentiometer and the rheostat.
Mastering this is your key to understanding everything from the joystick on your game controller and the throttle on an e-scooter to the gas pedal sensor in a modern car.
The Voltage Divider (The "Tapping Point")
A voltage divider is just a series circuit, but we use it to "tap" a lower voltage from a higher one. Instead of doing a bunch of math, we can use a slick shortcut.
The Voltage Divider Rule: V_x = V_Source * (R_x / R_Total)
This instantly finds the voltage (V_x) across any single resistor (R_x) in a series circuit.
The Potentiometer: An Adjustable Voltage Divider
A potentiometer ("pot" for short) is the real-world version of this. It's a resistor with three terminals: two ends (Input and Ground) and a "wiper" that moves between them.
Familiar App: A Gaming Controller Joystick: Ever wonder how your character moves? The joystick uses two potentiometers—one for the X-axis (left/right) and one for the Y-axis (up/down). When you move the stick, you're moving the wipers. This sends a changing voltage signal to the console, telling it exactly how far and in what direction you're pushing. "Stick drift" is often just a worn-out potentiometer!
Professional App: A Car's Throttle Position Sensor (TPS): This is the exact same principle as the joystick, but for a car. The car's computer (ECU) sends 5V to the TPS. Pressing the gas pedal moves a wiper, sending a variable voltage back to the ECU to tell it how much power to send to the engine.
The Current Divider (The "Flow Splitter")
A current divider is a parallel circuit. The rule is a shortcut to find how the total current splits between the branches.
The Current Divider Rule: I_x = I_Total * (R_Total / R_x)
Heads Up! Notice the formula is "inverted." You use the total resistance over the branch resistance. This is because more current goes down the path of least resistance.
The Rheostat: An Adjustable Current Controller
A rheostat is a variable resistor used to control the total current. It only has two terminals. You can make one by wiring a pot's wiper to one of its ends.
Familiar App: An LED Dimmer: If you have dimmable LED light strips in your car or room, the dimmer knob is often a rheostat. As you turn it, you're changing the resistance in series with the LEDs. More resistance = less current = dimmer lights. Less resistance = more current = brighter lights.
Professional App: Industrial Motor Speed Control: This uses the exact same principle, but on a bigger scale. A large, high-power rheostat controls the current flowing to a DC motor on a machine. You are directly controlling the rate of flow to manage the motor's speed.
Let's put these shortcuts to work.
Voltage Divider Example:
A 24V source is connected to a 100Ω and a 200Ω resistor in series. What is the voltage across the 200Ω resistor?
Old way: Find R_Total (300Ω), find I_Total (24V/300Ω=0.08A), find V_200 (0.08A*200Ω=16V).
New way (Voltage Divider Rule):
V_200 = 24V * (200Ω / (100Ω + 200Ω))
V_200 = 24V * (200 / 300) = 16V. Done in one step.
Current Divider Example:
10 Amps of total current enters a parallel junction that splits into two branches: Branch A (2Ω) and Branch B (8Ω). How much current goes down Branch A?
First, find R_Total of the parallel section: 1/R_Total = 1/2 + 1/8 = 5/8 -> R_Total = 8/5 = 1.6Ω.
Now, use the Current Divider Rule:
I_A = 10A * (1.6Ω / 2Ω)
I_A = 10A * 0.8 = 8A. As expected, the path of lower resistance gets the most current.
You're a technician. A car comes in with poor acceleration and erratic shifting. The codes point to a fault in the Throttle Position Sensor (TPS). How do you confirm the diagnosis? This is the same logic you'd use to diagnose "stick drift" on a faulty game controller.
The "Sweep Test" - Evaluating a Potentiometer
The most common failure in a potentiometer is a "dead spot" on the resistive track caused by wear.
The Plan: You'll use a multimeter to measure the output voltage from the TPS wiper while a helper slowly and smoothly presses the gas pedal.
The Analysis (What to Expect): A good TPS should show a smooth voltage change, for example, from 0.5V up to 4.5V without any sudden jumps or drops.
The Fault Finding: As your helper presses the pedal, you watch the multimeter. The voltage climbs smoothly: 1.2V... 1.5V... 1.8V... then suddenly it drops to 0V or jumps to 5V before continuing to climb. That's the dead spot. You have just evaluated the component's performance and proven it is faulty. The ECU sees that sudden voltage drop as you taking your foot off the gas, causing the engine to hesitate.
Scenario: An old factory conveyor belt uses a large rheostat to control its speed. The motor now only runs at full speed, or not at all, no matter where the control knob is set.
A rookie might just order a new motor. A pro creates a diagnostic plan.
Your Diagnostic Plan:
Hypothesize: The symptoms suggest the rheostat is no longer able to vary the resistance. It's likely "failed open." When bypassed it works, otherwise it doesn't.
Create a Test Procedure:
Step 1 (Safety): Lock out power to the entire system.
Step 2 (Isolate): Disconnect the two wires leading to the rheostat.
Step 3 (Test): Set your multimeter to measure resistance (Ohms). Connect your leads to the two terminals of the rheostat.
Step 4 (Measure & Verify): Slowly turn the control knob from minimum to maximum. You should see the resistance value change smoothly (e.g., from 0Ω up to its max rating, say 500Ω).
Step 5 (Confirm the Fault): In this case, you measure "OL" (Over Limit/Infinite) on your meter, no matter where the knob is. This confirms your hypothesis: the internal resistive wire has broken. The rheostat is bad.
The Solution: You have created a non-destructive test plan, proven the fault is in the controller and not the motor, and can now confidently order the correct replacement part.
(Remembering)
What is the name for a 3-terminal variable resistor used as an adjustable voltage divider?
To use a potentiometer as a 2-terminal rheostat, which terminal must be connected to one of the outer terminals?
(Understanding)
3. Explain why adding a rheostat in series with a motor allows you to control the motor's speed.
4. If a technician sees a voltage signal from a sensor suddenly drop to zero and then return to normal as it's being tested, what does this indicate about the component?
(Applying)
5. A 12V source is connected to two series resistors: R1 is 1kΩ and R2 is 3kΩ. Use the Voltage Divider Rule to calculate the voltage drop across R2.
6. A total current of 5A flows into a parallel circuit with two branches. Branch 1 has a resistance of 10Ω and Branch 2 has a resistance of 15Ω. Use the Current Divider Rule to find the current flowing through Branch 1.
(Analyzing)
7. A technician tests a TPS. At idle, it reads 0.5V (correct). At wide-open throttle, it reads 5.0V (correct is ~4.5V). What is the most likely internal fault in the sensor that would cause this specific reading? (Hint: Think about the three terminals).
8. In an industrial motor circuit, a rheostat is used to control speed. A technician notices the rheostat is getting extremely hot. Analyzing the situation, would increasing or decreasing the motor's load (how hard it's working) likely cause the rheostat to get hotter? Explain your reasoning.
(Evaluating)
9. A technician needs to get a 3V signal from a 12V source. They have a box full of 1kΩ resistors. They propose building a voltage divider using four 1kΩ resistors in series. Evaluate this solution. Is it a valid way to get 3V? Justify your answer.
(Creating)
10. The right joystick on a video game controller is causing the character to move randomly up and down even when it's not being touched ("stick drift"). Create a logical hypothesis for the fault and a safe, simple test plan to confirm it, assuming you can get access to the potentiometer's terminals inside the controller.
Various circuits using basic electrical kits, mobile modular, control circuit panels