Answer:
Resistance, R = 8624.18 ohms
Explanation:
It is given that,
The emf of the circuit, [tex]V_o=12\ V[/tex]
Capacitance of the capacitor, [tex]C=110\ \mu F=110\times 10^{-6}\ F[/tex]
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 :
[tex]V=V_o(1-e^{\dfrac{-t}{RC}})[/tex]
[tex]e^{\dfrac{-t}{RC}}=1-\dfrac{V}{V_o}[/tex]
[tex]e^{\dfrac{-t}{RC}}=1-\dfrac{10}{12}[/tex]
[tex]e^{\dfrac{-t}{RC}}=0.1666[/tex]
[tex]\dfrac{-1.7}{RC}=ln(0.1666)=-1.792[/tex]
[tex]R=\dfrac{1.7}{1.792\times 110\times 10^{-6}}[/tex]
[tex]R=8624.18\ \Omega[/tex]
So, the value of resistance used in the charging circuit is 8624.18 ohms. Hence, this is the required solution.
