PHYSICS 1250 PACKAGE >CI<
PHYSICS 1250 PACKAGE >CI<
9th Edition
ISBN: 9781305000988
Author: SERWAY
Publisher: CENGAGE LEARNING (CUSTOM)
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Chapter 32, Problem 32.54P

(a)

To determine

The energy stored in the capacitor at any time t .

(a)

Expert Solution
Check Mark

Answer to Problem 32.54P

The energy stored in the capacitor at any time t=2.00ms is 4.29J .

Explanation of Solution

Given info: The inductance of the inductor is 3.30H , the capacitance of the capacitor is 840pF , the initial charge of the capacitor is 105μC and the time is 2.00ms .

Formula to calculate the angular frequency of the LC circuit is,

ω=1LC

Substitute 3.30H for L and 840pF of C to find the ω .

ω=1(3.30H)840pF(1012F1pF)=1.8×104s

Formula to calculate the energy stored in the capacitor at any time t is,

Ec=Q(t)22C (1)

Formula to calculate the instantaneous value of the charge is,

Q(t)=Qmaxcosωt

Here,

Q(t) is the instantaneous value of the charge.

Qmax is the maximum charge of the capacitor.

ω is the angular frequency.

t is the time.

Substitute Qmaxcosωt for Q(t) in equation (1).

Ec=(Qmaxcosωt)22C (2)

Here,

Ec is the energy stored in the capacitor at any time t .

Substitute 105μC for Qmax , 1.8×104s for ω , 840pF of C and 2.00ms for t in the  equation (2) to find the Ec .

Ec=(105μC(106C1μC)cos((1.8×104s)2.00ms(103s1ms)))22×840pF(1012F1pF)=4.29J

Thus, the energy stored in the capacitor at any time t=2.00ms is 4.29J .

Conclusion:

Therefore, the energy stored in the capacitor at t=2.00ms is 4.29J .

(b)

To determine

The energy stored in the inductor at any time t .

(b)

Expert Solution
Check Mark

Answer to Problem 32.54P

The energy stored in the capacitor at any time t=2.00ms is 2.03.J .

Explanation of Solution

Given info: The inductance of the inductor is 3.30H , the capacitance of the capacitor is 840pF and the initial charge of the capacitor is 105μC and the time is 2.00ms .

Formula to calculate the current in the circuit is,

i(t)=dQ(t)dt

Substitute Qmaxcosωt for Q(t) .

i(t)=d(Qmaxcosωt)dt=ωQmaxsinωt

Formula to calculate the energy stored in the inductor at ant time t is,

EI=12Li(t) (3)

Here,

EI is the energy stored in the inductor.

i(t) is the current at time t .

Substitute ωQmaxsinωt for i(t) in equation (3).

EI=12L(ωQmaxsinωt)2 (4)

Substitute 105μC for Qmax , 1.8×104rad/s for ω , 3.30H for L and 2.00ms for t in the  equation (4) to find the U .

EI=123.30H((1.8×104rad/s)105μC(106C1μC)sin(1.8×104s)2.00ms(103s1ms))2=2.03.J

Thus, the energy stored in the capacitor at any time t=2.00ms is 2.03.J .

Conclusion:

Therefore, the energy stored in the capacitor at any time t=2.00ms is 2.03.J .

(c)

To determine

The total energy in the circuit.

(c)

Expert Solution
Check Mark

Answer to Problem 32.54P

The total energy in the circuit is 6.56J .

Explanation of Solution

Given info: The inductance of the inductor is 3.30H , the capacitance of the capacitor is 840pF and the initial charge of the capacitor is 105μC and the time is 2.00ms .

Formula to calculate the total energy in the circuit is,

E=(Qmax)22C

Here,

E is the total energy in the circuit.

Substitute 105μC for Qmax and 840pF for C to find the EC .

E=(105μC(106C1μC))22×840pF(1012F1pF)=6.56J

Thus, the total energy in the circuit is 6.56J .

Conclusion:

Therefore, the total energy in the circuit is 6.56J .

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Chapter 32 Solutions

PHYSICS 1250 PACKAGE >CI<

Ch. 32 - Prob. 32.6OQCh. 32 - Prob. 32.7OQCh. 32 - Prob. 32.1CQCh. 32 - Prob. 32.2CQCh. 32 - A switch controls the current in a circuit that...Ch. 32 - Prob. 32.4CQCh. 32 - Prob. 32.5CQCh. 32 - Prob. 32.6CQCh. 32 - The open switch in Figure CQ32.7 is thrown closed...Ch. 32 - After the switch is dosed in the LC circuit shown...Ch. 32 - Prob. 32.9CQCh. 32 - Discuss the similarities between the energy stored...Ch. 32 - Prob. 32.1PCh. 32 - Prob. 32.2PCh. 32 - Prob. 32.3PCh. 32 - Prob. 32.4PCh. 32 - An emf of 24.0 mV Ls induced in a 500-turn coil...Ch. 32 - Prob. 32.6PCh. 32 - Prob. 32.7PCh. 32 - Prob. 32.8PCh. 32 - Prob. 32.9PCh. 32 - Prob. 32.10PCh. 32 - Prob. 32.11PCh. 32 - A toroid has a major radius R and a minor radius r...Ch. 32 - Prob. 32.13PCh. 32 - Prob. 32.14PCh. 32 - Prob. 32.15PCh. 32 - Prob. 32.16PCh. 32 - Prob. 32.17PCh. 32 - Prob. 32.18PCh. 32 - Prob. 32.19PCh. 32 - When the switch in Figure P32.18 is closed, the...Ch. 32 - Prob. 32.21PCh. 32 - Show that i = Iiet/ is a solution of the...Ch. 32 - Prob. 32.23PCh. 32 - Consider the circuit in Figure P32.18, taking =...Ch. 32 - Prob. 32.25PCh. 32 - The switch in Figure P31.15 is open for t 0 and...Ch. 32 - Prob. 32.27PCh. 32 - Prob. 32.28PCh. 32 - Prob. 32.29PCh. 32 - Two ideal inductors, L1 and L2, have zero internal...Ch. 32 - Prob. 32.31PCh. 32 - Prob. 32.32PCh. 32 - Prob. 32.33PCh. 32 - Prob. 32.34PCh. 32 - Prob. 32.35PCh. 32 - Complete the calculation in Example 31.3 by...Ch. 32 - Prob. 32.37PCh. 32 - A flat coil of wire has an inductance of 40.0 mH...Ch. 32 - Prob. 32.39PCh. 32 - Prob. 32.40PCh. 32 - Prob. 32.41PCh. 32 - Prob. 32.42PCh. 32 - Prob. 32.43PCh. 32 - Prob. 32.44PCh. 32 - Prob. 32.45PCh. 32 - Prob. 32.46PCh. 32 - In the circuit of Figure P31.29, the battery emf...Ch. 32 - A 1.05-H inductor is connected in series with a...Ch. 32 - A 1.00-F capacitor is charged by a 40.0-V power...Ch. 32 - Calculate the inductance of an LC circuit that...Ch. 32 - An LC circuit consists of a 20.0-mH inductor and a...Ch. 32 - Prob. 32.52PCh. 32 - Prob. 32.53PCh. 32 - Prob. 32.54PCh. 32 - An LC circuit like the one in Figure CQ32.8...Ch. 32 - Show that Equation 32.28 in the text Ls Kirchhoffs...Ch. 32 - In Figure 31.15, let R = 7.60 , L = 2.20 mH, and C...Ch. 32 - Consider an LC circuit in which L = 500 mH and C=...Ch. 32 - Electrical oscillations are initiated in a series...Ch. 32 - Review. Consider a capacitor with vacuum between...Ch. 32 - Prob. 32.61APCh. 32 - An inductor having inductance I. and a capacitor...Ch. 32 - A capacitor in a series LC circuit has an initial...Ch. 32 - Prob. 32.64APCh. 32 - When the current in the portion of the circuit...Ch. 32 - At the moment t = 0, a 24.0-V battery is connected...Ch. 32 - Prob. 32.67APCh. 32 - Prob. 32.68APCh. 32 - Prob. 32.69APCh. 32 - At t = 0, the open switch in Figure P31.46 is...Ch. 32 - Prob. 32.71APCh. 32 - Prob. 32.72APCh. 32 - Review. A novel method of storing energy has been...Ch. 32 - Prob. 32.74APCh. 32 - Review. The use of superconductors has been...Ch. 32 - Review. A fundamental property of a type 1...Ch. 32 - Prob. 32.77APCh. 32 - In earlier times when many households received...Ch. 32 - Assume the magnitude of the magnetic field outside...Ch. 32 - Prob. 32.80CPCh. 32 - To prevent damage from arcing in an electric...Ch. 32 - One application of an RL circuit is the generation...Ch. 32 - Prob. 32.83CP
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