Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
9th Edition
ISBN: 9781259989452
Author: Hayt
Publisher: Mcgraw Hill Publishers
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Chapter 9, Problem 43E
To determine
Find the equation for current and evaluate at time
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Consider the RLC circuit shown where the initial current flowing through the circuit at time t = 0 is I_0 = 5 and the initial charge on the capacitor at time t = 0 is Q_0 = 2. The components have values of R = 100 ohms, L = 5 H, and C = 1/450,500 F.
Write the differential equation for Q(t), the charge across the capacitor, assuming the voltage source V(t) = 0
The voltage pulse applied to the 100 mH inductor shown is 0 for t<0 and is given by the expressionv(t)=20te−10t V for t>0. Also assume i=0 for t≤0.. Find the inductor current as a function of time.
(Draw the diagram) Consider the RC circuit in which R=0.5 Ω, C=0.1 F, and E=20 V. Given that the capacitor has zero initial charge, determine the current in the circuit after 0.25 seconds.
Chapter 9 Solutions
Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
Ch. 9.1 - A parallel RLC circuit contains a 100 2 resistor...Ch. 9.2 - After being open for a long time, the switch in...Ch. 9.2 - Prob. 3PCh. 9.2 - Prob. 4PCh. 9.3 - (a) Choose R1 in the circuit of Fig. 9.14 so that...Ch. 9.4 - Prob. 6PCh. 9.5 - Prob. 7PCh. 9.5 - Prob. 8PCh. 9.6 - Let is = 10u(t) 20u(t) A in Fig. 9.31. Find (a)...Ch. 9.6 - Let vs = 10 + 20u(t) V in the circuit of Fig....
Ch. 9.7 - Alter the capacitor value and voltage source in...Ch. 9 - For a certain source-free parallel RLC circuit, R...Ch. 9 - Element values of 10 mF and 2 nH are employed in...Ch. 9 - If a parallel RLC circuit is constructed from...Ch. 9 - Prob. 4ECh. 9 - You go to construct the circuit in Exercise 1,...Ch. 9 - A parallel RLC circuit has inductance 2 mH and...Ch. 9 - Prob. 7ECh. 9 - A parallel RLC circuit has R = 1 k, L = 50 mH. and...Ch. 9 - Prob. 9ECh. 9 - Prob. 10ECh. 9 - The current flowing through a 5 resistor in a...Ch. 9 - For the circuit of Fig.9.40, obtain an expression...Ch. 9 - Consider the circuit depicted in Fig. 9.40. (a)...Ch. 9 - With regard to the circuit represented in Fig....Ch. 9 - (a) Assuming the passive sign convention, obtain...Ch. 9 - With regard to the circuit presented in Fig. 9.42,...Ch. 9 - Obtain expressions for the current i(t) and...Ch. 9 - FIGURE 9.43 Replace the 14 resistor in the...Ch. 9 - Design a complete source-free parallel RLC circuit...Ch. 9 - For the circuit represented by Fig. 9.44, the two...Ch. 9 - Prob. 21ECh. 9 - Prob. 22ECh. 9 - A critically damped parallel RLC circuit is...Ch. 9 - A source-free parallel RLC circuit has an initial...Ch. 9 - A critically damped parallel RLC circuit is...Ch. 9 - For the circuit of Fig. 9.45, is(t) = 30u(t) mA....Ch. 9 - Prob. 27ECh. 9 - The circuit of Fig. 9.44 is rebuilt such that the...Ch. 9 - Prob. 29ECh. 9 - Prob. 30ECh. 9 - The source-free circuit depicted in Fig. 9.1 is...Ch. 9 - (a) Graph the current i for the circuit described...Ch. 9 - Analyze the circuit described in Exercise 31 to...Ch. 9 - A source-free parallel RLC circuit has capacitance...Ch. 9 - Prob. 35ECh. 9 - Obtain an expression for vL(t), t 0, for the...Ch. 9 - For the circuit of Fig. 9.47, determine (a) the...Ch. 9 - (a) Design a parallel RLC circuit that provides a...Ch. 9 - The circuit depicted in Fig. 9.48 is just barely...Ch. 9 - When constructing the circuit of Fig. 9.48, you...Ch. 9 - The circuit of Fig. 9.22a is constructed with a...Ch. 9 - Prob. 42ECh. 9 - Prob. 43ECh. 9 - The simple three-element series RLC circuit of...Ch. 9 - Prob. 45ECh. 9 - Prob. 46ECh. 9 - Prob. 47ECh. 9 - With reference to the series RLC circuit of Fig....Ch. 9 - Obtain an expression for i1 as labeled in Fig....Ch. 9 - The circuit in Fig. 9.52 has the switch in...Ch. 9 - For the circuit in Fig. 9.52, determine the value...Ch. 9 - In the series circuit of Fig. 9.53, set R = 1 ....Ch. 9 - Evaluate the derivative of each current and...Ch. 9 - Consider the circuit depicted in Fig. 9.55. If...Ch. 9 - Prob. 55ECh. 9 - In the circuit shown in Fig. 9.56, (a) obtain an...Ch. 9 - Prob. 57ECh. 9 - For the circuit represented in Fig. 9.57, (a)...Ch. 9 - FIGURE 9.57 Replace the 1 resistor in Fig. 9.57...Ch. 9 - A circuit has an inductive load of 2 H, a...Ch. 9 - (a) Adjust the value of the 3 resistor in the...Ch. 9 - Determine expressions for vC(t) and iL(t) in Fig....Ch. 9 - The capacitor in the LC circuit in Fig. 9.60 has...Ch. 9 - Suppose that the switch in the circuit in Fig....Ch. 9 - The capacitor in the circuit of Fig. 9.63 is set...Ch. 9 - The physical behavior of automotive suspension...Ch. 9 - A lossless LC circuit can be used to provide...
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- A resistor (R = 1 Ω), inductor (L = 0.1 H) and capacitor (C = 0.1 F) are connected in series, and the current I(t) through the circuit is measured as shown in the image below Assuming that the capacitor is uncharged at t = 0, and that the circuit is electrically small (such that propagation times between components can be neglected), find (or approximate where necessary) for times t = [0 : 0.1 : 0.4] (i.e. do not calculate at t = 0.5) : (shown in the image below)arrow_forwardA series circuit has a capacitor of 1.5625x10^(-8)F a resistor of 2x10^4 ohms, and an inductor of 1H. If the initial charge on the capacitor is zero,. if a 12-volt battery is connected to the circuit and the circuit is closed at t=0, determine the charge on the capacitor at any time tarrow_forwardFor the circuit shown below, which of the following is equal to the current ic(t) flowing through the capacitor at time t < 0?arrow_forward
- The voltage pulse applied to the 100 mH inductor shown is 0 for t<0. and is given by the expression v(t)=20te−10t V for t>0. Also assume i=0 for t≤0. Sketch the voltage as a function of time.arrow_forwardA 20μF capacitor is subjected to a voltage pulse having a duration of 1 s. The pulse is described by the following equations: vc(t)={30t2 V,0≤t≤0.5 s;30(t−1)2 V,0.5 s≤t≤1 s;0elsewhere. Sketch the current pulse that exists in the capacitor during the 1 s interval.arrow_forwardWhy is the following situation impossible? The LC circuit as shown has L = 30.0 μH and C = 50.0 μF. The capacitor has an initial charge of 200 μC. The switch is closed, and the circuit undergoes undamped LC oscillations. At periodic instants, the energies stored by the capacitor and the inductor are equal, with each of the two components storing 250 μJ.arrow_forward
- Calculate initial conditions for inductor current and capacitor voltage in circuit presented in Fig. 8.3. Assume: L=1H, C=0.5F, R=1Ω, e(t) = 10 2 sin(t + 45 ) V, i(t) = 2sin(t − 45 ) A.arrow_forwardSuppose the input to the circuit is a damped ramp of the form Kte−100t V. Find the largest value of K such that the inductor current does not exceed the 40 mA current ratingarrow_forward*The resistance, inductance, and capacitance in a parallel RLC circuit are 1900 Ω , 250 mH , and 9 nF , respectively. * Pt A. Calculate the minimum root of the characteristic equation that describes the voltage response of the circuit. Pt B. Calculate the maximum root of the characteristic equation that describes the voltage response of the circuit. Pt C.Will the response be over-, under-, or critically damped? Pt D. What value of R will yield a damped frequency of 12 krad/s? Pt E. What are the roots of the characteristic equation for the value of R found in Part D? Pt F. What value of R will result in a critically damped response?arrow_forward
- *Assume that at the instant the 2 A dc current source is applied to the circuit in (Figure 1), the initial current in the 25 mH inductor is 1 A, and the initial voltage on the capacitor is 50 V (positive at the upper terminal).* Pt A. Find the expression for iL(t) for t≥0 if R equals 12.5 Ωarrow_forwardConsider the given circuit. The switch has been closed for a very long time before opening at t=0s. Determine the capacitor voltage (in volts) right before the switch has been opened, the time constant of the circuit for t>0 (in ms), and the expression for the capacitor voltage for t≥0.arrow_forwardIn response to a change introduced by a switch at t = 0, the current flowing through a 100 μF capacitor, defined in accordance with the passive sign convention, was observed to be i(t) = −0.4e−0.5t mA (for t > 0). If the final energy stored in the capacitor (at t = ∞) is 0.2 mJ, determine υ(t) for t ≥ 0.arrow_forward
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