Lecture 9_v2 - dt dV C C dt dV C dt dV C I I I + = + = + =...

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Spring 2011 ECE 2100, A. Molnar, Cornell University 1 Lecture 9 Capacitors
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Spring 2011 ECE 2100, A. Molnar, Cornell University 2 Governing equations Q + - + - + - + - + - + - + - () () 0 1 0 V d I C V dt dV C dt dQ I d A C C Q V A Q d V A Q E t + = = = = ττ / / / / + V - I Separated charge Æ Electric field Æ voltage Define Capacitance: Farads: F=s/ Derivative of charge Æ current, proportional to derivative of voltage
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Spring 2011 ECE 2100, A. Molnar, Cornell University 3 V(t) C Examples + V - I(t) C I I(t) V(t) 1ms 2ms 1 μ A μ A 1V 0V 1 μ F 1nF V(t) V=0 V=t*10kV/s V=10V 10kV/s 10mA I(t) P(t) W(t) 2 2 0 2 50 2 100 10 10 ms J t CV d d dV CV W W t dt dV CV VI P mA I s kV t V t / μ τ = = = = = = = = 1ms 100mw 50 μ J
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Spring 2011 ECE 2100, A. Molnar, Cornell University 4 Equivalents () () () 2 1 2 2 2 1 2 2 2 1 2 1 2 1 C C C I I dt dV C C dt dV C I I
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Unformatted text preview: dt dV C C dt dV C dt dV C I I I + = + = + = + = + = dt dV C C C dt dV dt dV C C C C dt dV C dt dV C C C C I C C C C I C I C I dt dV dt dV dt dV dt dV V V V dt dV C dt dV C I + = + = + = + = + = + = + = = = 2 1 1 2 2 1 1 2 2 2 2 1 1 2 2 1 1 2 2 1 2 1 2 1 2 1 V(t) C1 C2 I I2 C1+C2 parallel Series C 1 C 2 I(t) Current-divider V 2 + 2 1 1 2 C C C C Voltage-divider + V-...
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Lecture 9_v2 - dt dV C C dt dV C dt dV C I I I + = + = + =...

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