A series circuit has a 0.1 henry inductor, a 310 ohm resistor, and a 0.000008 farad capacitor. There is an initial charge of 0.000003 coulombs, there is no initial current, and there is an applied voltage which is described as . Identify the solution to the differential equation that describes the charge on the capacitor as a function of time.

Question

A series circuit has a 0.1 henry inductor, a 310 ohm resistor, and a 0.000008 farad capacitor. There is an initial charge of 0.000003 coulombs, there is no initial current, and there is an applied voltage which is described as  . Identify the solution to the differential equation that describes the charge on the capacitor as a function of time.

Quizplus · Accepted Answer

The differential equation that describes the charge on the capacitor as a function of time is:

Q'' + (R/L)Q' + (1/LC)Q = (1/L)*V

where Q is the charge on the capacitor, R is the resistance, L is the inductance, C is the capacitance, and V is the applied voltage.

Plugging in the given values, we get:

Q'' + (310/0.1)Q' + (1/(0.1*0.000008))Q = (1/0.1)*11eaa88b_9288_a33b_a696_ff5c4d859646_TB5869_11

Simplifying and solving for Q, we get:

Q(t) = (11eaa88b_9288_f15e_a696_23d035aa6666_TB5869_11)exp(-1550t) + (11eaa88b_9289_186f_a696_972aa392201c_TB5869_11)exp(-200t)

where t is time.

Thus, the answer is (C).

A Series Circuit Has a 0