Question

1. In an oscillating *LC* circuit with *C* = 77.2
μF, the current is given by *i* = (2.09) sin(3710*t*
+ 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 *μ*F capacitor. Initially the capacitor
has a charge of 6.3 *μ*C 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(3710*t* + 0.878)
has its maximum value of "1" , hence

sin(3710*t* + 0.878) = 1

sin(3710*t* + 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 i^{2}_{max} = (0.5)
(9.4 x 10^{-4}) (2.09)^{2} = 0.00205 J

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