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A charging RC circuit controls the intermittent windshield wipers in a car. The emf is 12.0 V. The wipers are triggered when the voltage across the 125 mu or micro F capacitor reaches 10.0 V; then the capacitor is quickly discharged (through a much smaller resistor) and the cycle repeats. What resistance should be used in the charging circuit if the wipers are to operate once every 1.80 s?

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Answer:

[tex]R=803k\Omega[/tex]

Explanation:

We have the following information,

[tex]V_0 = 12V\\V=10V\\c= 1.25*10^{-6}F\\t=1.8s[/tex]

We apply the equation for capacitor charging the voltage across it,

[tex]V=V_0 (1-e^{-t/x})\\e^{-t/x}=1-(\frac{V}{V_0})\\-\frac{t}{Rc}=ln(\frac{V}{V_0})\\R=-\frac{t}{ln(\frac{V}{V_0})*c}[/tex]

Replacing values,

[tex]R=-\frac{1.8}{ln(10/12)*1.25*10^{-6}}[/tex]

[tex]R=803k\Omega[/tex]

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