Electrical Circuits (AC)


Previously Asked Questions

Q:     A particular experiment requires a beam of light of very stable intensity.  Why would AC voltage be unacceptable for powering the light?

A:    The light emitted by a light bulb is due to heating of the bulb's filament when electric current passes through it.  In order to achieve light emission of high stability.  A constant current is needed.  This cannot be provided by an AC current, since the AC current varies in time.

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References

Equations

Oscillating LC circuit energy transfers
33-1.gif (177 bytes)   and   33-2.gif (164 bytes)

(U = UE + UB)

Differential equation of LC oscillation (with no resistance)

Differential Equation

33-11.gif (259 bytes)

Solution
33-12.gif (201 bytes)
Charge amplitude (maximum charge on capacitor) Q
Angular frequency (omega2.gif (834 bytes)) of the oscillations 33-4.gif (183 bytes)
Current (i) of the system 33-13.gif (212 bytes)
Damped oscillations
Differential Equation


33-20.gif (382 bytes)

Solution
33-21.gif (267 bytes)

for

33-22.gif (251 bytes)

For small R, omega2.gif (834 bytes)' approx.gif (53 bytes) omega2.gif (834 bytes) and the maximum energy of the electric field in the capacitor is 33-24.gif (230 bytes)
External alternating emf causing a series RLC circuit to be set into forced oscillations at a driving angular frequency (omega2.gif (834 bytes)d) 33-25.gif (158 bytes)
Current driven in the RLC circuit by the emf 33-26.gif (200 bytes)
Series RLC circuit current amplitude 33-51.gif (675 bytes)
Series RLC circuit phase constant 33-56.gif (239 bytes)
Series RLC circuit impedance (Z) 33-52.gif (274 bytes)
Series RLC circuit current amplitude (rewritten) I = varepsilon.gif (50 bytes) m/Z
Average power (Pav) 33-62.gif (301 bytes)

"rms" stands for root-mean-square.   "rms" quantities are related to maximum quantities by xrms = x /sqrt2.gif (84 bytes)
So Irms = I /sqrt2.gif (84 bytes),   Vrms = V /sqrt2.gif (84 bytes),  and  varepsilon.gif (50 bytes)rms = varepsilon.gif (50 bytes) /sqrt2.gif (84 bytes), and

Transformation of voltage 33-70.gif (217 bytes)
Transformation of currents 33-71.gif (202 bytes)
Equivalent resistance of the secondary circuit in a transformer as seen by the generator 33-73.gif (285 bytes)

[Top] [Previously Asked Questions] [References]


List of Topics

Measurements Electric Potential Magnetism Electrical Circuits (AC) Optical Instruments: Mirrors and Lenses
Electrostatics Capacitance Sources of Magnetic Fields Maxwell's Equations Interference
Electric Fields Current and Resistance Magnetism in Matter Electromagnetic Waves Diffraction
Electric Flux Electrical Circuits (DC) Electromagnetic Induction Interaction of Radiation with Matter: Reflection, Refraction, Polarization  

 

 

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