The timing device in an automobile’s intermittent wiper system is based on an RC time constant and utilizes a 0.350 µF capacitor and a varia

Question

The timing device in an automobile’s intermittent wiper system is based on an RC time constant and utilizes a 0.350 µF capacitor and a variable resistor. Over what range (in MΩ) must R be made to vary to achieve time constants from 2.50 to 17.0 s?

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Thu Giang 1 week 2021-07-21T04:47:35+00:00 1 Answers 1 views 0

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    2021-07-21T04:49:14+00:00

    Answer:

    Explanation:

    Given that,

    Capacitance of the capacitor is

    C = 0.350 µF = 0.35 × 10^-6 F

    Time constant ranges from

    τ(min) = 2.5s

    τ(max) = 17s

    We want to find the range the resistance

    Now, using the time constant formulae

    τ = RC

    Then, R= τ/C

    So,

    R(min) = τ(min) /C

    R(min) = 2.5 / 0.35 × 10^-6

    R(min) = 7.143 × 10^6 Ω

    R(min) = 7.143 MΩ

    R(max) = τ(max) /C

    R(max) = 17 / 0.35 × 10^-6

    R(max) = 48.57 × 10^6 Ω

    R(max) = 48.57 MΩ

    So the resistance ranges from

    7.143 MΩ < R < 48.57 MΩ

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