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6 March, 06:33

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.

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  1. 6 March, 06:35
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    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.
  2. 6 March, 06:52
    0
    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.
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