Lec2008_08 - Sinusoidal response of RC circuits When both...

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Sinusoidal response of RC circuits When both resistance and capacitance are in a series circuit, the phase angle between the applied voltage and total current is between 0 ° and 90 ° , depending on the values of resistance and reactance. V R V V R leads V S V C lags V S C R C V I S I V S Lecture 8 Lecture 8-1 Electronics and Laboratory
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Impedance and phase angle of series RC circuits Impedance : the total opposition to sinusoidal current Phase angle : phase difference between the total current and the source voltage In a series RC circuit, the total impedance is the phasor sum of R and X C . R is plotted along the positive x -axis. X C is plotted along the negative y -axis. R 1 tan C X R θ ⎛⎞ = ⎜⎟ ⎝⎠ R the θ θ X C Z X C Z Z is the diagonal 2 2 X R Z + = Lecture 8 Lecture 8-2 Electronics and Laboratory C
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Analysis of series RC circuits Ohm’s law is applied to series RC circuits using Z , V , and I . VV VI ZI Z I = == Because I is the same everywhere in a series circuit, you can obtain the voltages across different components by multiplying the impedance of at component by the current as shown in the following example that component by the current as shown in the following example. ssume the current is 10 mA s Sketch the voltage phasor diagram. Assume the current is 10 mA rms . Sketch the voltage phasor diagram. The voltage phasor diagram can be found from Ohm’s law. Multiply each impedance phasor by 10 mA. V R = 12 V x 10 mA R = 1.2 k Ω 9 9 θ θ V C = 6 V = X C = 960 Ω = 1.33 k 39 o = 13.3 V 39 o Lecture 8 Lecture 8-3 Electronics and Laboratory 9.6 V Z 1.33 k Ω S
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Analysis of series RC circuits (2) Phase relation of the voltages and current in a series RC circuit V R θ I = C V 1 n X C 1 n R V tan θ = R tan V C V S 2 2 C R S V V V + = Lecture 8 Lecture 8-4 Electronics and Laboratory Voltage and current phasor diagram
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Variation of impedance and phase angle with frequency Phasor diagrams that have reactance phasors can only be drawn for a single frequency because X is a function of frequency. creasing R As frequency changes, the impedance triangle for an RC circuit changes as illustrated here θ Z 3 1 2 3 Increasing f θ θ because X C decreases with increasing f . This determines the equency response f C ircuits. X C 3 Z 2 f 3 frequency response of RC circuits. X C 2 Z 1 2 f X C 1 1 f Lecture 8 Lecture 8-5 Electronics and Laboratory
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RC lag and lead circuits C lag circuit (low ass filter) V R RC lag circuit (low-pass filter) θ φ V R C V out V in V out (phase lag) φ V out V in V in RC lead circuit (high-pass filter) θ (phase lead) V V out C V in θ R V C V out V in V in V out Lecture 8 Lecture 8-6 Electronics and Laboratory
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Impedance and phase angle of parallel RC circuits
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Lec2008_08 - Sinusoidal response of RC circuits When both...

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