Explanation Given info: The capacitance of the circuit is 5.00 μf , the inductance of the circuit is 2.00 mH the resistance is 10 Ω and the emf of the battery is 12.0 V . For the long time the circuit was at point a so the steady state current is, i = ε R Here, ε is the emf of the battery. R is the resistance of the circuit. Substitute 12.0 V for ε and 10 Ω for R in the above equation. i = 12.0 V 10.0 Ω = 1.2 A Thus, the steady state current is 1.2 A . The resonant frequency of the LC circuit is, ω = 1 L C Here, L is the inductance C is the capacitance Substitute 2.00 mH for L and 5.00 μf for C in the above equation. ω = 1 ( 2.00 mH ) ( 5.00 μf ) = 1 ( 2.00 mH × 1 H 1000 mH ) ( 5.00 μf × 1 f 10 6 μf ) = 10 4 rads Thus, the resonance frequency is 10 4 rads . The charge in the LC circuit is given by, q = q max cos ( ω t + ϕ ) Here, q max is the maximum charge in the circuit. ω is the resonant frequency. ϕ is the phase of the circuit. Fort time t = 0 s the charge in the circuit is zero. Substitute 0 for q and 0 for t in the above equation. q max cos ( ω t + ϕ ) = 0 cos ( w ( 0 ) + ϕ ) = 0 ϕ = π 2 Thus, the charge equation is, q = q max cos ( ω t + π 2 ) = − q max sin ( ω t ) Differentiate the above equation with respect to t

10th Edition

ISBN: 9781337553278

Author: Raymond A. Serway, John W. Jewett

Publisher: Cengage Learning

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Chapter 31, Problem 43AP

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The current in the capacitor in the circuit after 1 s .

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Chapter 31, Problem 42AP

Chapter 31, Problem 44AP

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Ch. 31.1 - A coil with zero resistance has its ends labeled a...Ch. 31.2 - Prob. 31.2QQ Ch. 31.3 - Prob. 31.3QQ Ch. 31.4 - Prob. 31.4QQ Ch. 31.5 - (i) At an instant of time during the oscillations...Ch. 31 - Prob. 1P Ch. 31 - Prob. 2P Ch. 31 - An emf of 24.0 mV Ls induced in a 500-turn coil...Ch. 31 - Prob. 4P Ch. 31 - Prob. 5P

Ch. 31 - A toroid has a major radius R and a minor radius r...Ch. 31 - Prob. 7P Ch. 31 - Prob. 8P Ch. 31 - Prob. 9P Ch. 31 - Prob. 10P Ch. 31 - Prob. 11P Ch. 31 - Show that i = Iiet/ is a solution of the...Ch. 31 - Prob. 13P Ch. 31 - You are working as a demonstration assistant for a...Ch. 31 - Prob. 15P Ch. 31 - The switch in Figure P31.15 is open for t 0 and...Ch. 31 - Prob. 17P Ch. 31 - Two ideal inductors, L1 and L2, have zero internal...Ch. 31 - Prob. 19P Ch. 31 - Prob. 20P Ch. 31 - Prob. 21P Ch. 31 - Complete the calculation in Example 31.3 by...Ch. 31 - Prob. 23P Ch. 31 - A flat coil of wire has an inductance of 40.0 mH...Ch. 31 - Prob. 25P Ch. 31 - Prob. 26P Ch. 31 - Prob. 27P Ch. 31 - Prob. 28P Ch. 31 - In the circuit of Figure P31.29, the battery emf...Ch. 31 - Prob. 30P Ch. 31 - An LC circuit consists of a 20.0-mH inductor and a...Ch. 31 - Prob. 32P Ch. 31 - In Figure 31.15, let R = 7.60 , L = 2.20 mH, and C...Ch. 31 - Prob. 34P Ch. 31 - Electrical oscillations are initiated in a series...Ch. 31 - Review. Consider a capacitor with vacuum between...Ch. 31 - A capacitor in a series LC circuit has an initial...Ch. 31 - Prob. 38AP Ch. 31 - Prob. 39AP Ch. 31 - At the moment t = 0, a 24.0-V battery is connected...Ch. 31 - Prob. 41AP Ch. 31 - You are working on an LC circuit for an experiment...Ch. 31 - Prob. 43AP Ch. 31 - Prob. 44AP Ch. 31 - Prob. 45AP Ch. 31 - At t = 0, the open switch in Figure P31.46 is...Ch. 31 - Review. The use of superconductors has been...Ch. 31 - Review. A fundamental property of a type 1...Ch. 31 - Prob. 49AP Ch. 31 - In earlier times when many households received...Ch. 31 - Assume the magnitude of the magnetic field outside...Ch. 31 - Prob. 52CP Ch. 31 - Prob. 53CP

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