Ch 31 Sol spr 08

# Ch 31 Sol spr 08 - ALTERNATING CURRENT 31 31.6 IDENTIFY The...

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A LTERNATING C URRENT 31.6. IDENTIFY: The reactance of capacitors and inductors depends on the angular frequency at which they are operated, as well as their capacitance or inductance. SET UP: The reactances are 1/ C XC and L XL . EXECUTE: (a) Equating the reactances gives 11 L C LC  (b) Using the numerical values we get (5.00 mH)(3.50 F) LC μ  = 7560 rad/s X C = X L = L = (7560 rad/s)(5.00 mH) = 37.8 Ω EVALUATE: At other angular frequencies, the two reactances could be very different. 31.12. IDENTIFY: Compare C v that is given in the problem to the general form sin C I vt C and determine . SET UP: 1 C X C . R v iR and cos . iI EXECUTE: (a) 6 1736 (120 rad s)(4.80 10 F) C X C (b) 3 7.60 V 4.378 10 A 1736 C C V I X and 3 cos (4.378 10 A)cos[(120 rad/s) ]. i I t t Then 3 (4.38 10 A)(250 )cos((120 rad s) ) (1.10 V)cos((120 rad s) ). R v iR t t EVALUATE: The voltage across the resistor has a different phase than the voltage across the capacitor. 31.19. IDENTIFY: Apply the equations in Section 31.3. SET UP: 250 rad/s, 200 , R  0.400 H, L 6.00 F C and 30.0 V. V EXECUTE: (a) 22 ( 1/ ) . Z R L C 2 6 2 (200 ) ((250 rad/s)(0.0400 H) 1/((250 rad/s)(6.00 10 F))) 601 Z (b) 30 V 0.0499 A. 601 V I Z (c) 1/ 100 667 arctan arctan 70.6 , 200 LC R        and the voltage lags the current. (d) (0.0499 A)(200 ) 9.98 V; R V IR   (0.0499 A)(250 rad s)(0.400 H) 4.99 V; L V I L 6 (0.0499 A) 33.3 V. (250 rad/s)(6.00 10 F) C I V C EVALUATE: (e) At any instant, . R C L v v v v  But C v and L v are 180 ° out of phase, so C v can be larger than v at a value of t , if LR vv is negative at that t .

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Ch 31 Sol spr 08 - ALTERNATING CURRENT 31 31.6 IDENTIFY The...

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