Question

Chapter 31, Problem 015 An oscillating LC circuit consisting of a 0.85 nF capacitor and a 3.7 mH coil has a maximum voltage of 2.7 V. What are (a) the maximum charge on the capacitor, (b) the maximum current through the circuit, (c) the maximum energy stored in the magnetic field of the coil? (a) Number (b) Number (c) Number Units Units Units

Answer 1

Solution) C = 0.85 nF = 0.85×10^(-9) F

L = 3.7 mH = 3.7×10^(-3) H

Vm = 2.7 V

(a) Maximum charge , Q = ?

Q = CVm

Q = 0.85×10^(-9)×2.7

Q = 2.295×10^(-9) C

Q = 2.3×10^(-9) C

Q = 2.3 nC

(b) i = ?

Maximum current occurs when

(Q^2)/(2C) = (1/2)(L)(i^2)

i^2 = (Q^2)/(LC)

i^2 = ((2.3×10^(-9))^2)/(3.7×10^(-3)×0.85×10^(-9))

i^2 = 1.68×10^(-6)

i = (1.68×10^(-6))^(1/2)

i = 1.296×10^(-3) A

i = 1.3 × 10^(-3) A

i = 1.3 mA

(c) Maximum energy stored in magnetic field , U = ?

U = (1/2)(L)(i^2)

U = (1/2)(3.7×10^(-3))(1.3×10^(-3))^2

U = 3.126×10^(-9)

U = 3.13×10^(-6) J