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?

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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