AC i-V relationship for R, L, and C

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AC i-V relationship for R, L, and C
Source vS(t) Asinwt
Resistive Load
VR and iR are in phase
Phasor representation vS(t) Asinwt
Acos(wt-90) A ?-90VS(jw)
IS(jw) (A / R)?-90
Impendence complex number of resistance
ZVS(jw)/ IS(jw)R
Generalized Ohms law VS(jw) Z
IS(jw) Everything we learnt before applies for
phasors with generalized ohms law
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Capacitor Load
ICE
VC(jw) A ?-90
Notice the impedance of a capacitance decreases
with increasing frequency
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Inductive Load
ELI
Phasor VL(jw)A ?-90 IL(jw)(A/wL)
?-180 ZLjwL
Opposite to ZC, ZL increases with frequency
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AC circuit analysis

• Effective impedance example
• Procedure to solve a problem
• Identify the sinusoidal and note the excitation
  frequency.
• Covert the source(s) to phasor form
• Represent each circuit element by its impedance
• Solve the resulting phasor circuit using previous
  learnt analysis tools
• Convert the (phasor form) answer to its time
  domain equivalent.

Ex. 4.16, p180
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Ex. 4.21 P188
R1100 W, R275 W, C 1mF, L0.5 H,
vS(t)15cos(1500t) V. Determine i1(t) and
i2(t). Step 1 vS(t)15cos(1500t), w1500
rad/s. Step 2 VS(jw)15 ?0 Step 3 ZR1R1,
ZR2R2, ZC1/jwC, ZLjwL Step 4 mesh equation