# AC Circuit

## An alternating current - AC - is generated by a sinusoidal voltage source

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An alternating current - *AC* - is generated by a sinusoidal voltage source.

### Ohm's Law

*U _{z} = I_{z} Z (1)*

*where*

*U _{z} = voltage drop over the load (volts, V) *

*I _{z }= current through the load (ampere, A)*

*Z = impedance of the load (ohms, Ω)*

### Voltage

The momentary voltage in an AC circuit as function of time can be expressed as

*u(t) = U _{max} sin(ω t + θ) (2)*

*where *

*u(t) = voltage in the circuit at time t (V)*

*U _{max} = maximal voltage at the amplitude of sine (V)*

*t = time (s)*

*ω = 2 π f *

* = angular frequency of sine wave (rad/s) *

*f = frequency (Hz, 1/s)*

*θ = phase of sine wave (rad)*

The momentary current as a function of time can be expressed as

*i(t) = I _{max} sin(ω t + θ) (2b)*

*where *

*i(t) = current at time t (A)*

* I _{max} *= maximal current at the amplitude of sine (A)

### RMS or Effective Voltage

RMS - Root Mean Square - or effective voltage of an AC sine wave can be expressed as

*U _{RMS} = U_{eff} *

* = U _{max} / (2)^{1/2} *

* = 0.707 U _{max }(3)*

*where *

*U _{RMS}* = RMS voltage (V)

*U _{max}* = maximum voltage (amplitude) of sinusoidal voltage source (V)

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