Transformers

• The relationship between the number of turns and the potential difference is governed by the Transformer Equation:

$\frac{V_p}{V_s} = \frac{n_p}{n_s}$

• Where $V_p$ and $V_s$ are the primary and secondary voltages, and $n_p$ and $n_s$ are the number of turns on the respective coils.

• For an ideal transformer (100% efficient), the input power equals the output power ($P = VI$):

$V_p I_p = V_s I_s$

• This implies that if the voltage is stepped up, the current must be stepped down proportionally to conserve energy.

• Transformers are categorized based on their effect on the input voltage, determined by the ratio of turns between the two coils.

• Transmission Efficiency: Electricity is transmitted at very high voltages (up to 400,000V) to minimize energy loss. High voltage results in a very low current for the same power level.

• Heating Losses: Since power loss in cables is calculated as $P = I^2R$, reducing the current significantly reduces the energy dissipated as heat in the transmission wires.

• Safety and Utility: Step-down transformers are used at local substations to reduce the voltage to safe levels (e.g., 230V) for use in consumer electronics and appliances.

• Check the Units: Always ensure that voltages are in Volts (V) and currents are in Amps (A) before substituting into the power equation.

• Ratio Consistency: When using the transformer equation, ensure the 'p' values are both on top or both on the bottom; mixing them up is a common source of calculation errors.

• Terminology Precision: Use the term turns when referring to the loops of wire and coils when referring to the entire primary or secondary component.

• Sanity Check: If you are calculating for a step-up transformer, your final $V_s$ must be larger than $V_p$. If it is smaller, you likely inverted your ratio.