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 110 µF 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 1.70 s?

Answer 1

Answer:

Resistance, R = 8624.18 ohms

Explanation:

It is given that,

The emf of the circuit, $V_o=12\ V$

Capacitance of the capacitor, $C=110\ \mu F=110\times 10^{-6}\ F$

Voltage across the capacitor, V = 10 V

Time for which the wipers are to operate. The formula for the voltage across the voltage is given by :

$V=V_o(1-e^{\dfrac{-t}{RC}})$

$e^{\dfrac{-t}{RC}}=1-\dfrac{V}{V_o}$

$e^{\dfrac{-t}{RC}}=1-\dfrac{10}{12}$

$e^{\dfrac{-t}{RC}}=0.1666$

$\dfrac{-1.7}{RC}=ln(0.1666)=-1.792$

$R=\dfrac{1.7}{1.792\times 110\times 10^{-6}}$

$R=8624.18\ \Omega$

So, the value of resistance used in the charging circuit is 8624.18 ohms. Hence, this is the required solution.