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A.C. summary

Sinusoidal a.c.: $$I=I_{0}\sin(\omega t)$$

  • Peak power loss $$P_{0}=I_{0}^{2}R=V_{0}^{2}/R$$

Root mean square (rms) ($$y_{\text{rms}}=\sqrt{\langle y^{2} \rangle}$$):

  • Sinusoidal wave : $$I_{\text{rms}}=\frac{I_{0}}{\sqrt 2}\quad \text{and} \quad V_{\text{rms}}=\frac{V_{0}}{\sqrt 2}$$

  • Square wave: $$I_{\text{rms}}=I_{0} \quad \text{and} \quad V_{\text{rms}}=V_{0}$$

  • Mean power loss: $$\langle P \rangle=I_{\text{rms}}^{2}R=\frac{V_{\text{rms}}^{2}}{R}$$

Transformer converts high/low voltage a.c. to low/high voltage a.c.

  • Primary coil connected to a.c. supply/Secondary coil connected to output terminals.

  • Step-up transformer: $$V_{\text{p}}\lt V_{\text{s}}$$/Step-down transformer: $$V_{\text{s}}\lt V_{\text{p}}$$

$$$\frac{V_{\text{s}}}{V_{\text{p}}}=\frac{N_{\text{s}}}{N_{\text{p}}}$$$

Ideal transformer: no power loss

$$$\frac{V_{\text{s}}}{V_{\text{p}}}=\frac{N_{\text{s}}}{N_{\text{p}}}=\frac{I_{\text{p}}}{I_{\text{s}}}$$$

Rectification: convert a.c. into d.c.

  • Half-wave rectification: One diode cancels negative current flow: $$I_{\text{rms, rec}}= I_{\text{rms}}\quad \text{and} \quad V_{\text{rms}, \text{ rec}} = V_{\text{rms}}$$

  • Full-wave rectification: Several diodes to restore both opposite current flows: $$I_{\text{rms}, \text{ half rec}} = \frac{I_{\text{rms}}}{\sqrt{2}}\quad \text{and} \quad V_{\text{rms}, \text{ half rec}} = \frac{V_{\text{rms}}}{\sqrt{2}}$$

$$V_{0}$$, $$I_{0}=$$peak voltage and current (maximal values)

$$N_{\text{p}}$$, $$N_{\text{s}}=$$ number of turns in the primary and secondary coils.