Question

1. In an oscillating LC circuit with C = 77.2 μF, the current is given by i = (2.09) sin(3710t + 0.878), where t is in seconds, i in amperes, and the phase angle in radians. (a) How soon after t = 0 will the current reach its maximum value? What are (b) the inductance L and (c) the total energy?

2. A single-loop circuit consists of a 7.2 Ω resistor, 11.9 H inductor, and a 3.2 μF capacitor. Initially the capacitor has a charge of 6.3 μC and the current is zero. Calculate the charge on
the capacitor N complete cycles later for (a) N = 5, (b) N =10, and (c) N = 100.

Answer 1

a)

current reach its maximum value when sin(3710t + 0.878) has its maximum value of "1" , hence

sin(3710t + 0.878) = 1

sin(3710t + 0.878) = Sin/2

3710 t + 0.878 = /2

t = 0.0001867 sec

t = 1.867 x 10^-4 sec

b)

C = Capacitance = 77.2 x 10^-6 F

L = inductance = ?

from the equation

w = 3710 rad/s

angular frequency is given as

w = 1/sqrt(LC)

3710 = 1/sqrt(LC)

3710 = 1/sqrt(L(77.2 x 10^-6))

L = 9.4 x 10^-4 H

c)

i_max= = maximum current = 2.09 A

maximum energy stored is given as

E_max = (0.5) L i²_max = (0.5) (9.4 x 10^-4) (2.09)² = 0.00205 J