(Solved): EXERCISE An uncharged capacitor and a resistor are connected in series to a battery, as shown in th ...

EXERCISE

An uncharged capacitor and a resistor are connected in series to a battery, as shown in the figure in the example, where  = 12.0 V, C = 40.5 µF, and R = 8.25 ? 10⁵ ?. The switch is moved to position a at 

t = 0.

 At what time (in s) is the charge on the capacitor equal to 2.43 ? 10^?4 C?

Charging a Capacitor in an RC Circuit An uncharged capacitor and a resistor are connected in series to a battery as shown in the figure, where & = 12.0 V, C = 5.80 ?F, and R = 7.30 x 105 . The switch is thrown to position a. Find the time constant of the circuit, the maximum charge on the capacitor, the maximum current in the circuit, and the charge and current as functions of time. A capacitor in series with a resistor, switch, and battery. Pb R + E When the switch is thrown to position a, the capacitor begins to charge up. 9b 3 www R When the switch is thrown to position b, the capacitor discharges. C E SOLUTION Conceptualize Study the figure and imagine throwing the switch to position a as shown in figure (b). Upon doing so, the capacitor begins to charge Categorize We evaluate our results using equations developed in this section, so we categorize this example as a substitution ? problem. Evaluate the time constant (in s) of the circuit from this equation: T = RC = 4.234 S Evaluate the maximum charge (in ?C) on the capacitor from this equation: Qmax = CE = 69.6 HC Evaluate the maximum current (in µA) in the circuit from this equation: E I? = 16.430 ?A R = www R E = 16.430 ?A R E Use these values in q(t) = CE(1 -t/RC - e-t/RC) = - e-t/RC) and i(t) = Qmax(1 e to find the charge and current as functions of time (Use the following as necessary: t. Assume q is in µC, i is in ?A, and t is in seconds. Do not enter units in your answers.): R (1) q(t) = (69.6(1-e-(+224)) (2) i(t) = 4.234 16.439 e EXERCISE An uncharged capacitor and a resistor are connected in series to a battery, as shown in the figure in the example, where & = 12.0 V, C = 40.5 µF, and R = 8.25 × 105 . The switch is moved to position a at t = 0. At what time (in s) is the charge on the capacitor equal to 2.43 x 10-4 C? Hint S Need Help? Read It Viewing Saved Work Revert to Last Response Submit Answer =