RC Circuits?

Question

A charging RC circuit controls the intermittent windshield wipers in a car. The emf is 12.0V. The wipers are triggered when the voltage across the 125(micro)F capacitor reaches 10.0V; 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 1.80s?

Answer 1

The voltage on the capacitor will behave the equation
v(t)=emf*(1-1/e^(t/T))

assuming the discharge time to be 0, the charge time is related to
10=12*(1-1/e^(1.8/T))
where T=R*C
1/e^(1.8/T)=1/6
e^(1.8/T)=6
1.8/T=ln(6)
T=1.8/(ln(6)

R*125*10^-6=1.8/ln(6)
R= 8 k ohms

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