Use the worked example above to help you solve this problem

Use the worked example above to help you solve this problem. An uncharged capacitor and a resistor are connected in series to a battery, as shown in the figure above. If epsilon = 14.0 V, C = 5.50 meuF, and R =- 7.90 x 105 omega, find the following. the time constant of the circuit the maximum charge on the capacitor the charge on the capacitor after 6.40 s the potential difference across the resistor after 6.40 s the current In the resistor at that time Use the values from PRACTICE IT to help you work this exercise. Find the charge on the capacitor after 1.80 6 have elapsed. Find the magnitude of the potential difference across the capacitor after l.80 s. Find the magnitude of the potential difference across the resistor at that same time.

Solution

A.

time constant: t = RC = 4.345 s

B.

maximum charge: Qmax = CVmax = 77 uC

C.

Charge on the capacitor: Q = C[V₀(1 - e^-t/RC)]

                                            = 59.348 uC
D.

Potential difference:

           dV = V-[V₀(1 - e^-t/RC)] = 3.2 V

E.

Current I = dV/R

---------------------------

a.

Charge: Q = Q_max [ 1 - e^-t/RC]

here, Qmax = CVmax

b.

potential difference: V = V₀ [ 1 - e^-t/RC], here, V₀ = e = 1 4V