Alternating Current

Voltage, current, and phase angle.  In general, the instantaneous voltage v=V\cos(\omega t+\phi) between two points in an ac circuit is not in phase with the instantaneous current i=I\cos\omega t passing through those points.

Resistance and reactance.  The voltage across a resistor is in phase with the current, V_R=IR.  The voltage across an inductor leads the the current by \frac\pi 2, V_L=IX_L, inductive reactance X_L=\omega L.  The voltage across a capacitor lags the the current by \frac\pi 2, V_C=IX_C, capacitive reactance X_C=\frac1{\omega C}.

Impedance and the L-R-C series circuit.  In general ac circuit, the voltage and current amplitutes are related by the circuit impedance Z, V=IZ.  In an L-R-C series circuit, Z=\sqrt{R^2+(\omega L-\frac1{\omega C})^2}, \tan\phi=\frac{\omega L-\frac1{\omega C}}R.

Power in ac circuits.  The average power input to an ac circuit: P_{av}=\frac12VI\cos\phi=V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi, where \phi is the phase angle of the voltage relative to the current.  The factor \cos\phi is called the power factor of the circuit.

Resonance angular frequencey.  \omega_0=\frac1{\sqrt{LC}}.

Transformers.  \frac{V_2}{V_1}=\frac{N_2}{N_1}, V_1I_1=V_2I_2.


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