# L9_sinusoidal_steadystate - ESC102 Introduction to...

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ESC102 : Introduction to Electronics A.R. Harish Dept. of EE, IIT Kanpur Sinusoidal Steady state Analysis Aug 10, 2010

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( ) cos( ) m v t V t ϖ θ = + ( ) ( ) Re( ) j t m v t V e ϖ θ + = × ( ) Re( cos( ) sin( )) m m v t V t jV t ϖ θ ϖ θ = + + + ( ) cos( ) m v t V t ϖ θ = + Re( ) m V t ϖ θ + m V θ Phasor ( ) cos( ) m v t V t ϖ θ = + 2 L8_sinusoidal_steadystate
Complex Impedances For the purpose of sinusoidal steady state analysis, inductors and capacitors can be represented as Complex Impedances 3 L9_sinusoidal_steadystate

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90 L M I I θ = ∠ - L M V LI ϖ θ = 90 90 L M V LI ϖ θ = ∠ - + 90 90 L M V I L θ ϖ = ∠ - × 90 L L V I L ϖ = × L L V I j L ϖ = × L L L V I Z = × L Z j L ϖ = This is like ohms law relationship between phasor voltage and current 5

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v(t) L=0.1H Example i(t) ( ) 2 cos(200 45) v t t = + 200 ϖ = 2 45 L V = ∠ L L L L V V I j L I j L ϖ ϖ = × = 2 45 2 45 0.1 45 20 20 90 L I j = = = ∠- ( ) 0.1 cos(200 45) i t t = - V rad/s V A A 6
v(t) L=0.1H Z L =j20 V 20 L L V I j = L Z j L ϖ = Carry out analysis with phasors keeping in mind that we can always transform phasor to the sinusoidal voltage or current as the case maybe.

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