The Transformer Equation

The fundamental principle states that the ratio of the voltages is directly proportional to the ratio of the number of turns in the coils.

This is expressed mathematically as: \frac{V_p}{V_s} = rac{n_p}{n_s}

Alternatively, the equation can be rearranged to solve for the secondary voltage: \frac{V_s}{V_p} = rac{n_s}{n_p}

This proportionality exists because the magnetic flux passing through each turn of wire is the same; therefore, more turns result in a higher total induced electromotive force (voltage).

An Ideal Transformer is assumed to be 100% efficient, meaning no energy is lost as heat due to resistance or magnetic hysteresis.

According to the Law of Conservation of Energy, the power input to the primary coil must equal the power output from the secondary coil in an ideal system.

Since electrical power is calculated as $P = V imes I$, the relationship for an ideal transformer is: $V_p imes I_p = V_s imes I_s$

This implies that if the voltage is stepped up (increased), the current must be stepped down (decreased) proportionally to maintain the same power level.

Check Your Ratios: Always ensure that if $n_s$ is larger than $n_p$, your calculated $V_s$ is also larger than $V_p$. This is a quick sanity check to avoid inversion errors.

Unit Consistency: Ensure all voltages are in Volts (V) and currents are in Amps (A). If a value is given in kV or mA, convert it to the base unit before using the equation.

Rearranging the Formula: If you are solving for a variable in the denominator, it is often easier to flip both sides of the equation first (e.g., use $\frac{V_s}{V_p} = \frac{n_s}{n_p}$ if solving for $V_s$).

Identify the Goal: Determine if the question asks for voltage, turns, or current. Remember that the power equation ($V_p I_p = V_s I_s$) is only used when current or power efficiency is mentioned.

DC vs. AC: A common mistake is assuming a transformer works with Direct Current (DC). Transformers require a changing magnetic field, which only Alternating Current (AC) provides.

Power Gain Myth: Students often mistakenly believe that a step-up transformer increases power. In reality, power stays the same (ideal) or decreases (real-world) because energy cannot be created.

Inverting the Ratio: Mixing up the primary and secondary values in the fraction is the most frequent calculation error. Always label your variables ($V_p, V_s, n_p, n_s$) clearly before starting.