## Exploration 30.3: Designing a Voltage Divider

RA = Ω | RA= x RB

Often with circuits, not only do you want to be able to figure out what a circuit that is already built is doing, you may want to design a circuit for a specific task. In this case our task is to design a circuit that is a voltage divider with a particular output voltage (voltage is given in volts and resistance is given in ohms). You have a 12-V supply that can give you 1 W of power, and you need a 4-V output with as much power as possible. The resistors that you have can dissipate 1 W of power. Restart.

To divide the voltage, we can put the power supply in series with two resistors and then use the voltage across one of the resistors to be our 4-V output.

1. What ratio of resistors do you need to divide the supply voltage by one third? In other words, how many times bigger (or smaller) should resistor A be than resistor B to get an output of 4 V? Try it.
2. Once the ratio is set up, do you have the maximum available power? To determine this, figure out the power used from the voltage source (P = V I). To get the maximum power (at a fixed voltage), should you increase or decrease the resistance in the circuit?
3. What is the limit on the total resistance (RA + RB) and, therefore, the limit on each resistor? Try it.
4. Try using a smaller value of resistance. Does the power supply burn up? (Fortunately, you can simply restart the animation and try again).
5. Double the values of RA and RB. How much power does this circuit now draw from the battery?

Now that you have determined convenient values of RA and RB that produce a 4-Volt output, replace the voltmeter with a lightbulb. (Adding a power-consuming circuit element is sometimes referred to as adding a "load.")

1. When this lightbulb is added, what is the voltage across the lightbulb?
2. Why is it less than 4 V?
3. If you increase RA and RB more, what happens to the voltage across the lightbulb? Why? This is the reason voltage dividers like this are made from resistors that are as small as possible.

Exploration authored by Anne J. Cox.
Script authored by Anne J. Cox and Wolfgang Christian.

Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.