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I am having trouble, the steady stae voltage i find by differential equations is no the same as the one i find by phasors, what is worng?

\$V_{ss}(t) = \cos(4t)\$ volts ........ by diff eq, just looking at thevinin voltage

phasor;$$V = 1\times\frac{-4j}{4\sqrt3 - 4j} = 0.5e^{-j\pi/3} = 1/2\cos(4t - \pi/3)$$

they are not the same, what is the problem?

enter image description here

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Thevnin voltage gives the open circuit voltage across two terminals (capacitor removed in this case). And\$V_{th} = \cos(4t)\$ in here.

schematic

When a load (capacitor in this case) is connected across these terminals, the voltage across the terminals A-B will change and you can use voltage division rule to obtain the output voltage. $$V_{AB} = V_{th}\times\dfrac{X_C}{R_{th}+X_C}$$ \$X_C\$-capacitive reactance.

The phasor method used you have used actually does that. So the answer is \$0.5\cos(4t-\pi/3)\$.

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  • \$\begingroup\$ but thevinine voltage is cos4t \$\endgroup\$ – user124627 Jul 5 '14 at 20:13
  • \$\begingroup\$ Thevinin voltage measured with capacitor removed is \$\cos 4t\$. When capacitor is connected, the voltage across these terminals will change. \$\endgroup\$ – nidhin Jul 6 '14 at 1:31

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