Question

You have a device that needs a voltage reference of 3.0 V, but you have only a 9.0 V battery. Fortunately, you also have several 10 k!1 resistors. Show how you can use the resistors and the battery to make a circuit that provides a potential difference of3.0 V.

Answer 1

Answer:

Explanation:

Solution:

- We are to develop a circuit that has an input of available battery 9.0 V and has an output potential difference of 3.0 V

- We are given:

             Battery ..... 9.0 V

             Resistors ... 10 Kohms

- We will develop a potential divider circuit by placing a few resistors in series and then connecting in between resistors to get our desired voltage.

- How many resistors should we use ?

  We know that if we add series resistance in a circuit the current decreases proportionally. However, the potential difference across resistors also changes.

- Our desired voltage is a ratio of input battery voltage.

                                   Input / Output = 9 / 3 = 3

We can use this ratio as the number of "Identical resistors" that can be placed in series to give us the desired voltage. Note: This would not be true if we did not had any identical resistors.

- We will place 3, 10 Kohms resistors in series.

- To verify we will calculate the potential difference across each resistor. The current of the total circuit is:

                                   I = V / R_eq

                                   R_eq = 3*R = 30 kohms

                                   I = 9 / 30,000 = 0.0003 Amps

- Now the potential difference for each resistor:

                                   V = I*R_each

                                   V = 0.0003*(10,000)

                                   V = 3.0 V

- We can take two leads across any 10 kohms resistor and the potential difference across the leads would be the desired voltage 3.0 V.

Answer 2

Given Information:

Input voltage = Vin = 9 V

Resistors = R = 10 kΩ each

Output voltage = Vout = 3 V

Required Information:

How many 10 kΩ resistors would it take = ?

Answer:

It would take three 10 kΩ resistors

Explanation:

We can make a voltage divider circuit that contains 3 resistors in series each having a value of 10 kΩ that will provide the desired voltage of 3 V.

Vout = Vin(R/Req)

If we choose 3 resistors of 10 kΩ each

Req = 10 + 10 + 10 = 30 kΩ

Vout = 9(10/30)

Vout = 9(1/3)

Vout = 3 V

Therefore, we would need three 10 kΩ resistors to get the desired voltage of 3 V.