Explanation 1) Concept: By using the relation between the potential difference across capacitor and time period, we can find the period of oscillation. After that, by using the concept of energy stored in the capacitor, we find the maximum energy stored in the capacitor. Similarly, we can find the maximum energy stored in the inductor, and from Faraday’s law, we can find the maximum rate of change of current. As the current is a function of time, we can find the maximum rate of gain of energy by inductor. 2) Formula: i) Voltage drop across the capacitor, V = I · X C ii) Period of oscillation, T = 2 π ω iii) Capacitive reactance, X C = 1 ω C iv) Maximum energy stored in the capacitor, U C = 1 2 · C V 2 v) Maximum energy stored in the inductor, U L = L i 2 2 vi) Magnitude of emf , V = ϵ = L d i d t vii) q = q 0 s i n ω t , charge on the plate of capacitor as function of time 3) Given: i) Current amplitude , I = q 0 ω = 7.50 m A = 7.50 × 10 - 3 A ii) Potential amplitude across capacitor , V = 250 m A = 250 × 10 - 3 A iii) Capacitance , C = 220 n F = 220 × 10 - 9 F 4) Calculations: a) The period of oscillation relation T = 2 π ω And we also have, V = I · X C = I ω C Hence we get ω = I V C using this in period relation we get T = 2 π ω T = 2 π I V C T = 2 π V C I T = 6.28 × 250 × 10 - 3 × 220 × 10 - 9 7.50 × 10 - 3 T = 46.1 × 10 - 6 s b) Maximum energy stored in the capacitor U C = 1 2 · C V 2 U = 0.5 × 220 × 10 - 9 × 250 2 × 10 - 6 U = 6.88 × 10 - 9 J c) Maximum energy stored in inductor U L = L i 2 2 We know that U c = 1 2 · C V 2 U c = L i 2 2 = U L Which gives L = C V 2 I 2 hence we get U L = C V 2 2 I 2 · I 2 U L = C V 2 2 = 6

11th Edition

ISBN: 9781119459170

Author: Halliday

Publisher: WILEY

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Chapter 31, Problem 18P

To determine

To find

a) Period of oscillation , T

b) Maximum energy stored in the capacitor , UC

c) Maximum energy stored in inductor , UL

d) Maximum rate of change of current , didtmaxi

e) Maximum rate of gain of energy by inductor , dULdtmaxi

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Chapter 31, Problem 17P

Chapter 31, Problem 19P

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Chapter 31 Solutions

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Ch. 31 - Figure 31-19 shows three oscillating LC circuits...Ch. 31 - Figure 31-20 shows graphs of capacitor voltage vc...Ch. 31 - Prob. 3Q Ch. 31 - What values of phase constant in Eq. 31-12 allow...Ch. 31 - Curve a in Fig. 31-21 gives the impedance Z of a...Ch. 31 - Prob. 6Q Ch. 31 - Prob. 7Q Ch. 31 - The values of the phase constant for four...Ch. 31 - Prob. 9Q Ch. 31 - Figure 31-24 shows three situations like those of...

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To find a) Period of oscillation , T b) Maximum energy stored in the capacitor , U C c) Maximum energy stored in inductor , U L d) Maximum rate of change of current , d i d t m a x i e) Maximum rate of gain of energy by inductor , d U L d t m a x i

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To find a) Period of oscillation , T b) Maximum energy stored in the capacitor , UC c) Maximum energy stored in inductor , UL d) Maximum rate of change of current , didtmaxi e) Maximum rate of gain of energy by inductor , dULdtmaxi

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Chapter 31 Solutions

To find

a) Period of oscillation , T

b) Maximum energy stored in the capacitor , UC

c) Maximum energy stored in inductor , UL

d) Maximum rate of change of current , didtmaxi

e) Maximum rate of gain of energy by inductor , dULdtmaxi