AC Alternating Current Physics Lesson 32 by Owen Borville 1.9.2026
While direct current (DC) is found in electrical systems where the source voltage is constant, alternating current (AC) is found in electrical systems where the source voltage varies periodically and in particular, sinusoidally.
The voltage source of an AC system produces a voltage that is calculated from the time, the peak voltage, and the angular frequency.
AC voltage = v = V0 sin ωt
AC current = i = I0 sin ωt
In a simple circuit, the current is found by dividing the voltage by the resistance. An AC current is calculated using the peak current (determined by dividing the peak voltage by the resistance), the angular frequency, and the time.
In resistors, the current through and the voltage across are in phase. In capacitors, when a sinusoidal voltage is applied to a capacitor, the voltage follows the current by one-fourth of a cycle. Since a capacitor can stop current when fully charged, it limits current and offers another form of AC resistance, called capacitive reactance, which has units of ohms.
Capacitive reactance = V0/I0 = 1/ωC = XC
In inductors in AC circuits, when a sinusoidal voltage is applied to an inductor, the voltage leads the current by one-fourth of a cycle. The opposition of an inductor to a change in current is expressed as a type of AC reactance. This inductive reactance, which has units of ohms, varies with the frequency of the AC source.
Inductive reactance = V0/I0 = ωL = XL
RLC series circuit is a resistor, capacitor, and inductor series combination across an AC source. The same current flows through each element of an RLC series circuit at all points in time.
The counterpart of resistance in a DC circuit is impedance, which measures the combined effect of resistors, capacitors, and inductors. The maximum current is defined by the AC version of Ohm's law. Impedance has units of ohms and is found using the resistance, the capacitive reactance, and the inductive reactance.
The AC version of Ohm's Law is I0 = V0/Z The impedance of an RLC series circuit = Z = √R^2 + (XL-XC)^2
The average AC power is found by multiplying the rms values of current and voltage. Ohm's law for the rms AC is found by dividing the rms voltage by the impedance. In an AC circuit, there is a phase angle between the source voltage and the current, which can be found by dividing the resistance by the impedance. The average power delivered to an RLC circuit is affected by the phase angle. The power factor ranges from (-1 to 1).
The average power associated with a circuit element is Pave = 1/2I0V0cosφ The average power dissipated by a resistor is Pave = 1/2I0V0 = IrmsVrms = Irms^2R
Vrms (rms voltage) = V0/√2
Irms (rms current) = Irms = I0/√2
The phase angle of an RLC series circuit = φ = tan-1(XL-XC)/R
At the resonance frequency, inductive reactance equals capacitive reactance. The average power versus angular frequency plot for a RLC circuit has a peak located at the resonant frequency. The sharpness or width of the peak is known as the bandwidth, which is related to a dimensionless quantity called the quality factor. A high quality factor value is a sharp or narrow peak.
The resonant angular frequency of a circuit is ω0 = √1/LC
The quality factor of a circuit is Q = ω0/Δω The quality factor of a circuit in terms of the circuit parameters is Q = ω0L/R
Electric power plants transmit high voltages at low currents to achieve lower ohmic losses in their many kilometers of transmission lines. Transformers use induction to transform voltages from one value to another. For a transformer, the voltages across the primary and secondary coils, or windings, are related by the transformer equation.
The transformer equation with voltage is Vs/Vp = Ns/Np
The currents in the primary and secondary windings are related by the number of primary and secondary loops, or turns, in the windings of the transformer. A step-up transformer increases voltage and decreases current, whereas a step-down transformer decreases voltage and increases current.
The transformer equation with current is Is = Np/Ns (Ip)
While direct current (DC) is found in electrical systems where the source voltage is constant, alternating current (AC) is found in electrical systems where the source voltage varies periodically and in particular, sinusoidally.
The voltage source of an AC system produces a voltage that is calculated from the time, the peak voltage, and the angular frequency.
AC voltage = v = V0 sin ωt
AC current = i = I0 sin ωt
In a simple circuit, the current is found by dividing the voltage by the resistance. An AC current is calculated using the peak current (determined by dividing the peak voltage by the resistance), the angular frequency, and the time.
In resistors, the current through and the voltage across are in phase. In capacitors, when a sinusoidal voltage is applied to a capacitor, the voltage follows the current by one-fourth of a cycle. Since a capacitor can stop current when fully charged, it limits current and offers another form of AC resistance, called capacitive reactance, which has units of ohms.
Capacitive reactance = V0/I0 = 1/ωC = XC
In inductors in AC circuits, when a sinusoidal voltage is applied to an inductor, the voltage leads the current by one-fourth of a cycle. The opposition of an inductor to a change in current is expressed as a type of AC reactance. This inductive reactance, which has units of ohms, varies with the frequency of the AC source.
Inductive reactance = V0/I0 = ωL = XL
RLC series circuit is a resistor, capacitor, and inductor series combination across an AC source. The same current flows through each element of an RLC series circuit at all points in time.
The counterpart of resistance in a DC circuit is impedance, which measures the combined effect of resistors, capacitors, and inductors. The maximum current is defined by the AC version of Ohm's law. Impedance has units of ohms and is found using the resistance, the capacitive reactance, and the inductive reactance.
The AC version of Ohm's Law is I0 = V0/Z The impedance of an RLC series circuit = Z = √R^2 + (XL-XC)^2
The average AC power is found by multiplying the rms values of current and voltage. Ohm's law for the rms AC is found by dividing the rms voltage by the impedance. In an AC circuit, there is a phase angle between the source voltage and the current, which can be found by dividing the resistance by the impedance. The average power delivered to an RLC circuit is affected by the phase angle. The power factor ranges from (-1 to 1).
The average power associated with a circuit element is Pave = 1/2I0V0cosφ The average power dissipated by a resistor is Pave = 1/2I0V0 = IrmsVrms = Irms^2R
Vrms (rms voltage) = V0/√2
Irms (rms current) = Irms = I0/√2
The phase angle of an RLC series circuit = φ = tan-1(XL-XC)/R
At the resonance frequency, inductive reactance equals capacitive reactance. The average power versus angular frequency plot for a RLC circuit has a peak located at the resonant frequency. The sharpness or width of the peak is known as the bandwidth, which is related to a dimensionless quantity called the quality factor. A high quality factor value is a sharp or narrow peak.
The resonant angular frequency of a circuit is ω0 = √1/LC
The quality factor of a circuit is Q = ω0/Δω The quality factor of a circuit in terms of the circuit parameters is Q = ω0L/R
Electric power plants transmit high voltages at low currents to achieve lower ohmic losses in their many kilometers of transmission lines. Transformers use induction to transform voltages from one value to another. For a transformer, the voltages across the primary and secondary coils, or windings, are related by the transformer equation.
The transformer equation with voltage is Vs/Vp = Ns/Np
The currents in the primary and secondary windings are related by the number of primary and secondary loops, or turns, in the windings of the transformer. A step-up transformer increases voltage and decreases current, whereas a step-down transformer decreases voltage and increases current.
The transformer equation with current is Is = Np/Ns (Ip)