CH3_Problems

# CH3_Problems - 1 57 Problems P roblems Section 3.1...

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Problems Section 3.1: Capacitance P3.1. What is a dielectric mat erial? Giv e two examples. P3.2. Briefly discuss how current can flow " through " a capacitor even though a non- conducting layer s eparates the metallic parts. P3.3. Describe the internal construction of capacitors. P3.4. What current flows through an ideal capacitor if the voltage across the capacitor is cons tant with time? To what circuit element is an ideal capacitor equivalent in circuits for which the currents and voltages are con s tant with time? *P3.5. A 2000 - JLF capacitor, initially charged to 100 V, is discharged by a stead y current of 100 JLA. How long doe s it tak e to dis charg e th e capacitor to 0 V? *P3.6. The voltage across a 10-JLF capacitor is given by v(t) = 100 sin(1000t). Find expressions for the current, power, and stored energy. Sketch the waveforms to scale versus time. *P3.7. A con s tant (de) current i( t) = 3 rnA flows into a 50-JLF capacitor. Th e voltage at t = 0 is v(O) = -20 V. Th e ref ere nce s for v(t) and i(t) have the passive configuration. Find the power at t = 0 and state whether the power flow is into or out of the capacitor. Repeat for t = 1 s. *P3.8. We want to store sufficient energ y in a 0.01-F capacitor to s upply 5 hor s epow er (hp) for one hour. To what voltage mu st th e capaci- tor be charged? (Note: 1 hp is equivalent to 745.7 W.) Doe s this s eem to be a practical method for storing this amount of ener gy? Do you think that an electric automobile design ba s ed on capacitive energy storage is feasible? P3.9. We have a 1-JLF capacitor with 200V betw ee n its terminals. Determine the magnitude of the net charge stored on each plate and the total net charge on both plates. P3.10. Suppose we have a 10-JLF capacitor and the voltage across it is given by vc (t) = 10 e- so ot. Problems 157 Find expre ssions for the current , power , and stored energ y. Sketch the waveforms to scale versus time. P3.11. Suppo se we hav e a 15-JLF capacitor that is charged to 500 V. Determine the initial stored charge and energy. If this capacitor is dis- charged to OV in a time interval of 4JLs , find the average power delivered by the capacitor during the discharge interval. P3.12. Starting at t = 0, the voltage across a 100- JLF capacitor is increased linearly with time to 200 V in 5 ms. Then , the voltage remains constant at 200 V. Sketch the voltage, current , power, and stored energy to scale versus time. P3.13. The current through a 2-JLF capacitor is shown in Figure P3.13. At t = 0, the voltage is zero. Sketch the voltage, power , and stored energy to scale ver sus time. ic(t) ic(t) ( rnA ) > 0 + 10 1--- vc(t) , , C = 2 J.LF 4 5 +-- -L 2 --~ r--l- t (ms) -20 ~ (a) (b) Figure P3.13 P3.14. Find the voltage, power , and stor ed energy at t = 20 ms for the capacitance in the circuit of Figure P3.14. + 5mA v(t) t = 0 Figure P3. 14 * D ~ not es that an swers ar e cont ained in th e Stud e nt So l ution s fi les. S ee Appendix F for mor e information a bout access in a th e S tud e nt SolutiOn s.

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