Current

Electric current

• Electric current is the flow of electric charge
• $I=\frac{dq}{dt}$
  • $I$ is the electric current of the circuit (in $\mathsf{A}$)
  • $q$ is the electric charge has passed through some surface in the circuit up to time $t$ (in $\mathsf{C}$)
  • $t$ is interval during which the charge flows (in $\mathsf{s}$)
• The SI unit of current is the ampere (abbreviated $\mathsf{amp}$ or $\mathsf{A}$), defined as $1\mathsf{A}=1C/s$
• A current is positive if it flows from the positive terminal of a voltage source to the negative terminal

Conventional current

• The conventional direction of current, also known as conventional current, is arbitrarily defined as the direction in which positive charges flow

  • electric current from $+$ to $-$ is equivalent to a negative electron flow from $-$ to $+$
  • conventional current combines the effects of electron, ion, proton, and hole flows all into one number.
  • Positive conventional current always flows from a high potential to a low potential.
  • conventional current is not the opposite of electron current
  • Electron current is a subset of conventional current.

• A 19th-century convention, still in use, treats any electric current as a flow of positive charge from a region of positive potential to one of negative potential.

  • The real motion, however, in the case of electrons flowing through a metal conductor, is in the opposite direction, from negative to positive.

Alternating Current (AC)

• $V=V_0\sin (\omega t)$ is the voltage of an alternating current (see sine wave)
  • $V_0$ is the peak voltage (in $\mathsf{V}$) (the amplitude)
  • $\omega =2\pi f$ is the angular frequency (in $rad/s$) where $f$ is the frequency (in $\mathsf{Hz}$)
  • $t$ is time (in $\mathsf{s}$)
• $I=\frac{V}{R}=\frac{V_0}{R}\sin (\omega t)=I_0\sin (\omega t)$ is the current of an alternating current
  • $I$ is the current (in $\mathsf{A}$)
  • $R$ is the resistance (in $\mathsf{\Omega }$)
  • $I_0$ is the peak current (in $\mathsf{A}$)
• $P=I^{2}R=I_0^{2}R{\sin }^2(\omega t)$ is the power transformed in a resistance $R$ at time $t$
  • Because the current is squared, the power is always positive
  • The average power is $\overline{P}=\frac{1}{2}{I}_0^{2}R$
• The rms values of sinusoidally alternating currents and voltages are:
  • $I_{\text{rms}}=\frac{I_0}{\sqrt{2}}$
  • $V_{\text{rms}}=\frac{V_0}{\sqrt{2}}$