laplace

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Explain the analysis of RLC network with and without initial condition with the help of laplace. 

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question 1

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Calculate the maximum DC voltage available from a half wave rectifier Shown . Also find the reading of the milli ammeter.  Solution:- Turn ratio of transformer = 20:1 Number of turns in primary binding = 20 Number of turns in secondary binding = 1 Mains voltage supply(1/p) Vp = 220 v From the Transformer ratio formula Np/Ns = Vp/Vs 20/1 = 220/ Vs Vs = 220/20 = 11V Vrms = Vm/√2  => Vm = Vrms √2 => Vm = 11 √2 Vm = 15.5563 v Vdc =  2Vm /π Vdc = 2×15.5563/π = 9.90V I = V/R => 9.90/1×1000 I = 9.90mA
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Trapezoidal rule 4

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Evaluate By (I) Trapezoidal rule ,  (ii) Simpson's one - third rule, correct to four decimals taking  h = 0.1 Solution :- h=0.1  Y = f(x)  X                   Y 0                    0 0.1                 0.00999 0.2                 0.03998 0.3                 0.08987 0.4                 0.15932 0.5                 0.24740 0.6                 0.35227 0.7                 0.47063 0.8                 0.59719 0.9                 0.72428 1.0                 0.84147 (I) Using Trapezoidal rule Integration of y dx = h/2 [( y0 + yn) + 2(y 1 + y 2 +.... ...... + y (n-1) ] => 0.1/2[(0 + 0.84147) + 2(0.00999 + 0.03998 + 0.08987 + 0.15932 + 0.24740+ 0.35227 + 0.47063 + 0.59719 + 0.72428) ] => 0.05 [ 0.84147 + 2× 2.69093 ] => 0.05 [ 0.84147 + 5.38186 ] => 0.05 × 6.22333 => 0.3111665 (ii)  Using Simpson's 1/3rd rule.  Integration of y dx = h/3  [( y 0 + y n ) + 4 (y 1 + y 3 +.... ...... + y(n-1) + 2(y 2+ y4 + .......... + y (n - 2)  ] => 0.1/3 [ ( 0 + 0.8414
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kinematics 12th

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  A body is thrown vertically upwards with an initial velocity u reaches the maximum height in 6s. The ratio of the distance traveled by the body in first second to seventh second is   Initial velocity u = g×t = 9.8 ×6 = 58.8 m/s   distance S 1 travelled in first second is calculated using " S = u ×t - (1/2)×g×t 2  ", using u = 58.8 m/s, and t = 1 s;   S 1  = 58.8 ×1 -(1/2) ×9.8 ×1 ×= 53.9 m   Since the paticle reaches maximum height in 6 s, at 7th second travel, its initial velocity is zero.   hence distance S 7  travelled in 7th second = (1/2) ×9.8 ×1 ×1 = 4.9 m   hence the ratio S 1  / S 7  = 53.9 / 4.9 = 11  
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