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Problems Week 10 - Problems —1 The pictures show two...

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Unformatted text preview: Problems: Week 10 10—1. The pictures show two oscillators. mflnl W X =1 O Electrical (El) Mechanical (Me) In Me the mass is at rest at x = 0 and the spring is relaxed. We pull M to x = A and release it, thereby causing oscillations. In El, first S] is closed, capacitor is charged to Q, then SI is opened and 32 is closed, again oscillations ensue. Write down the energy equations for the two systems and explain why the oscillations occur. 10-2. Shown are three circuits. In each case the output of the ac generator is g = 8m sin rot . We have learned that the , ' 8m ‘ ' ' ~81” ' ' currents arezk : $3111 (0t, 1C : ngwcos wt, 1L = L cos (01‘. Draw approprlate a) _ dlagrams to show that (1) 1/: IS In phase wrthg , (11) 10 is 3 ahead of 8 and (111) 1L IS 3 behind 8 . 10—3. The output of the generator is a a 6"" sin cot , 8m is fixedbut the frequency can be set by you. X is an unknown element. Identify X if on doubling the frequency the current (i) increases by a factor of 2, (ii) reduces by a factor of 2, (iii) remains unaltered. 10—4. ,8 =(1503inWt) Volts R = 1009 Calculate ' 1.. Root—mean square (r.m.s) voltage 2. Root mean square current 3, Energy absorbed by R per second. ‘ 10-5. The ac in your house has an r.m.s. voltage of 110-115V. What is the peak (maximum) voltage? 10~6. If 8 : 5(sin rot) Volts and f = 600Hz and im = 10“3 amp what is L? How much energy is absorbed by L in one cycle? Why? ' I 10—7. In the circuit of problem 10—6 replace L by C. If the current remains the same what is C? 10-8. In the circuit shown the current amplitude is gm 1 2 162+[wLm#] (0C —>0 bothwhen (0+0 Qua—>00. Why? 1 1:2 I” If you vary a), i I" 10-9. In the circuit of 10-8, the current is i = i," sin cut the potential is v = 8m sin(a)t + (D) where (0L _ L tan CD : ~—0)C R and 8 l 2 in, =41 with Z: R2 +[wL—— Z ‘ coC ’ Show that the average power absorbed is 2 < P >= i’i—cos2 (D 2R . . 1 . Hints: Averages < sm2 cat >: E, < sm wt cos cot >= 0 10-10. When Maxwell looked at the field equations ECE'M:IUUZII "(1) and [MD 2 E .-A€=— B ~2 lg he At () where (DB : 124 flux of 13 through area 4 and E NC is the non-coulomb E surrounding 4 ; he claimed that Eq ( 1) was “incomplete”. Do you notice the reason for his concern? V 10—1 1. What is the difference between a conduction current and a displacement current? ...
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