Question

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?

Answer 1

`R=803k\Omega`

Step-by-step explanation:

We have the following information,

`V_0 = 12V\\V=10V\\c= 1.25*10^(-6)F\\t=1.8s`

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

`V=V_0 (1-e^(-t/x))\\e^(-t/x)=1-((V)/(V_0))\\-(t)/(Rc)=ln((V)/(V_0))\\R=-(t)/(ln((V)/(V_0))*c)`

Replacing values,

`R=-(1.8)/(ln(10/12)*1.25*10^(-6))`

`R=803k\Omega`