{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ch06_ssm - 6 Inductance Capacitance and Mutual Inductance...

This preview shows pages 1–4. Sign up to view the full content.

6 Inductance, Capacitance, and Mutual Inductance Assessment Problems AP 6.1 [a] i g = 8 e 300 t 8 e 1200 t A v = L di g dt = 9 . 6 e 300 t + 38 . 4 e 1200 t V , t > 0 + v (0 + ) = 9 . 6 + 38 . 4 = 28 . 8 V [b] v = 0 when 38 . 4 e 1200 t = 9 . 6 e 300 t or t = (ln 4) / 900 = 1 . 54 ms [c] p = vi = 384 e 1500 t 76 . 8 e 600 t 307 . 2 e 2400 t W [d] dp dt = 0 when e 1800 t 12 . 5 e 900 t + 16 = 0 Let x = e 900 t and solve the quadratic x 2 12 . 5 x + 16 = 0 x = 1 . 45 , t = ln 1 . 45 900 = 411 . 05 µ s x = 11 . 05 , t = ln 11 . 05 900 = 2 . 67 ms p is maximum at t = 411 . 05 µ s [e] p max = 384 e 1 . 5(0 . 41105) 76 . 8 e 0 . 6(0 . 41105) 307 . 2 e 2 . 4(0 . 41105) = 32 . 72 W [f] i max = 8[ e 0 . 3(1 . 54) e 1 . 2(1 . 54) ] = 3 . 78 A w max = (1 / 2)(4 × 10 3 )(3 . 78) 2 = 28 . 6 mJ [g] W is max when i is max, i is max when di/dt is zero. When di/dt = 0 , v = 0 , therefore t = 1 . 54 ms. 6–1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
6–2 CHAPTER 6. Inductance, Capacitance, and Mutual Inductance AP 6.2 [a] i = C dv dt = 24 × 10 6 d dt [ e 15 , 000 t sin 30 , 000 t ] = [0 . 72 cos 30 , 000 t 0 . 36 sin 30 , 000 t ] e 15 , 000 t A , i (0 + ) = 0 . 72 A [b] i π 80 ms = 31 . 66 mA , v π 80 ms = 20 . 505 V , p = vi = 649 . 23 mW [c] w = 1 2 Cv 2 = 126 . 13 µ J AP 6.3 [a] v = 1 C t 0 i dx + v (0 ) = 1 0 . 6 × 10 6 t 0 3 cos 50 , 000 x dx = 100 sin 50 , 000 t V [b] p ( t ) = vi = [300 cos 50 , 000 t ] sin 50 , 000 t = 150 sin 100 , 000 t W , p (max) = 150 W [c] w (max) = 1 2 Cv 2 max = 0 . 30(100) 2 = 3000 µ J = 3 mJ AP 6.4 [a] L eq = 60(240) 300 = 48 mH [b] i (0 + ) = 3 + 5 = 2 A [c] i = 125 6 t 0 + ( 0 . 03 e 5 x ) dx 2 = 0 . 125 e 5 t 2 . 125 A [d] i 1 = 50 3 t 0 + ( 0 . 03 e 5 x ) dx + 3 = 0 . 1 e 5 t + 2 . 9 A i 2 = 25 6 t 0 + ( 0 . 03 e 5 x ) dx 5 = 0 . 025 e 5 t 5 . 025 A i 1 + i 2 = i AP 6.5 v 1 = 0 . 5 × 10 6 t 0 + 240 × 10 6 e 10 x dx 10 = 12 e 10 t + 2 V v 2 = 0 . 125 × 10 6 t 0 + 240 × 10 6 e 10 x dx 5 = 3 e 10 t 2 V v 1 ( ) = 2 V , v 2 ( ) = 2 V W = 1 2 (2)(4) + 1 2 (8)(4) × 10 6 = 20 µ J
Problems 6–3 AP 6.6 [a] Summing the voltages around mesh 1 yields 4 di 1 dt + 8 d ( i 2 + i g ) dt + 20( i 1 i 2 ) + 5( i 1 + i g ) = 0 or 4 di 1 dt + 25 i 1 + 8 di 2 dt 20 i 2 = 5 i g + 8 di g dt Summing the voltages around mesh 2 yields 16 d ( i 2 + i g ) dt + 8 di 1 dt + 20( i 2 i 1 ) + 780 i 2 = 0 or 8 di 1 dt 20 i 1 + 16 di 2 dt + 800 i 2 = 16 di g dt

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 10

ch06_ssm - 6 Inductance Capacitance and Mutual Inductance...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online