Alternating Current

12.1

Phase, lag and lead

PMDC: Describe the phase of alternating current and explain how phase lag and phase lead occur in AC circuits.

An AC current is $i=I_0$ sin($\omega$ t + $\varphi$). Phase $\varphi$ says where in the cycle you are at $t=0.$ Two waves can peak together (in phase) or one can peak later (lag) or earlier (lead).

In a resistor they peak together. In an inductor the current lags the voltage by $90^{\circ }$ (ELI: E then I in L). In a capacitor the current leads the voltage by $90^{\circ }$ (ICE: I then E in C).

• $i=I_0\sin (\omega t+\varphi )$
• R: V and I in phase
• L: I lags V by $90^{\circ }$ (ELI)
• C: I leads V by $90^{\circ }$ (ICE)

12.2

AC through R, C and L

PMDC: Explain the flow of AC through resistors, capacitors and inductors.

Resistor: $i=v$ / R at every instant. Power heats the resistor. No phase shift.

Capacitor: it is a gap, so DC stops after the plates fill. AC keeps charging and discharging, so current flows in the wires. Reactance $X_C$ = 1/($\omega$ C) falls as frequency rises — a capacitor is easy at high f, open at DC.

Inductor: changing current makes a back emf. Reactance $X_L=\omega$ L rises with frequency — a coil is a choke at high f, almost a short at DC.

• $R:i=v/R$
• $X_C=1/(\omega C)=1/(2\pi fC)$
• $X_L=\omega L=2\pi fL$
• $I_{rms}=I_0/\sqrt{2}{V}_{rms}=V_0/\sqrt{2}$

12.3

The EM spectrum

PMDC: Become familiar with the EM spectrum from radio waves to gamma rays.

All electromagnetic waves are oscillating E and B, perpendicular to each other and to the travel direction. In vacuum they all move at c. What changes is frequency (and so wavelength, and so photon energy).

In order of increasing frequency (decreasing wavelength): radio, microwave, infrared, visible, ultraviolet, X-rays, gamma rays.

• $c=f\lambda c=3\times 10^{8}m{s}^{-1}invacuum$
• radio → micro → IR → vis → UV → X → $\gamma$ (f ↑, $\lambda$ ↓)
• $E=h$ f (energy of one photon — Unit 14)