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Transformer basics

$$\frac{V_{\text{out}}}{V_{\text{in}}}=\frac{N_{\text{out}}}{N_{\text{in}}}$$

For example, $N_{\text{input}}=100,N_{\text{output}}=1000, V_{\text{in}}=20$ Write formula exactly, then sub in numbers $\to$ $V_{\text{out}}=2000V$!

Conservation of energy

Obviously this isn't magic and energy has to be conserved!

$$\begin{align} P_{\text{in}}=P_{\text{out}}\ (\text{Assuming 100\% efficiency} ) \\ V_{\text{in}}I_{\text{in}}=V_{\text{out}}I_{\text{out}} \\ \frac{V_{\text{out}}}{V_{\text{in}}}=\frac{I_{\text{in}}}{I_{\text{out}}} \\ \\ \text{Thus, inverse effect on current.} \\ \text{e.g. Increase } V \text{ by 1000x} \implies I \text{ decreases by 1000x} \end{align} $$

Well designed transformer will have close to $100%$ efficiency! (Because no moving parts, i.e. no friction)

Inefficiency