Question

An LC circuit consists of a 3.400 capacitor and a coil with self-inductance 0.080 H and no appreciable resistance. At t = 0 the capacitor is fully charged so the potential between the plates is 1.588 V and the current in the inductor is zero. What is the charge on the plates? How long after t = 0 will the current in the circuit be maximum? What will be the maximum current? What is the total energy in the system?

Answer 1

Step-by-step explanation:

charge on the capacitor = capacitance x potential

= 1.588 x 3.4

= 5.4 C

Energy of capacitor = 1 / 2 C V ² , C is capacitance , V is potential

= .5 x 3.4 x 1.588²

= 4.29 J

If I be maximum current

energy of inductor = 1/2 L I² , L is inductance of inductor .

energy of inductance = Energy of capacitor

1/2 L I² = 4.29

I² = 107.25

I = 10.35 A

Time period of oscillation

T = 2π √ LC

=2π √ .08 X 3.4

= 3.275 s

current in the inductor will be maximum in T / 4 time

= 3.275 / 4

= .819 s.

Total energy of the system

= initial energy of the capacitor

= 4.29 J