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# A.C. summary

## Main equations for a.c.

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.