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Unformatted text preview: 204 Chapter 4 Transients Note: You can check the answers to many of the problems in this chapter by using a computer aided circuitanalysis program such as Multisim Problems Section 4.1: FirstOrder RC Circuits P4.1. Suppose we have a capacitance C discharging through a resistance R. Define and give an expression for the time constant. To attain a long time constant, do we need large or small values for R? For C? *P4.2. The dielectric materials used in real capac itors are not perfect insulators. A resistance called a leakage resistance in parallel with the capacitance can model this imperfection. A 100~tF capacitor is initially charged to 100V. We want 90 percent of the initial energy to remain after one minute. What is the limit on the leakage resistance for this capacitor? *P4.3. The initial voltage across the capacitor shown in Figure P4.3 is vc(O+) = 10V. Find an expression for the voltage across the capaci tor as a function of time . Also, determine the time to at which the voltage crosses zero. t = 0 R =50 kQ + + vc(t) Figure P4.3 *P4.4. A 100~tF capacitance is initia ll y charged to 1000 V. At t = 0, it is connected to a 1kn resistance. At what time t2 has 50 percent of the initial energy stored in the capacitance been dissipated in the resistance? *P4 .5. At t = 0, a charged 10~tF capacitance is con nected to a voltmeter, as shown in Figure P4.5. The meter can be modeled as a resistance. At t = 0, the meter reads SOV. At t = 30s, from National Instruments or OrCAD Capture from Cadence Inc. See Appendix D for more information. the reading is 25 V. Find the resistance of the voltmeter. )I t t = 0 , ' VM Figure P4.5 *P4.6. At time t1, a capacitance Cis charged to a volt age of vl. Then, the capacitance discharges through a resistance R. Write an expression for the voltage across the capacitance as a function of time for t > t1 in terms of R, C, V1,andt1. P4.7. Given an initially charged capacitance that begins to discharge through a resistance at t = 0, what percentage of the initial voltage remains at two time constants? What percent age of the initial stored energy remains? P4 .8. The initial vo ltage across the capacitor shown in Figure P4.3 is vc(O+ ) = 0. Find an expres sion for the voltage across the capacitor as a function of time, and sketch to scale versus time. P4.9. In physics, the halflife is often used to characterize exponential decay of physical quantities such as radioactive substances. The halflife is the time required for the quantity to decay to half of its initial value. The time constant for the voltage on a capacitance dis charging through a resistance is r = RC. Find an expression for the halflife of the voltage in terms of R and C....
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This document was uploaded on 02/14/2012.
 Spring '09
 Mechatronics

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