Your portable lava lamp operates on 120-V AC power, but you're visiting a country with 240-V AC power. You plug a travel adapter into the 240-V AC outlet and its transformer provides your lamp with the 120-V AC power it expects. Compare the numbers of turns in the transformer's two coils.

The coil turns ratio in a transformer is fundamental to its operation. This ratio dictates how the transformer modifies the voltage from its primary coil (input) to its secondary coil (output). The equation describing this is \(\frac{V_p}{V_s} = \frac{N_p}{N_s}\). Here, \(V_p\) stands for the primary voltage and \(V_s\) for the secondary voltage. \(N_p\) and \(N_s\) signify the number of turns in the primary and secondary coils, respectively.

Using this equation, you can infer either the voltage change if the turns ratio is known, or the necessary number of coil turns if different input and output voltages are considered. For instance, in our problem, the turns ratio is calculated as 2:1 due to the voltage change from 240V to 120V. This means the primary coil has twice the number of turns as the secondary coil.

Remember, the turns ratio is crucial because it ensures that the transformer's secondary voltage matches your device's required voltage, thereby safeguarding it from damage.

Understanding the primary and secondary voltages is key to using a transformer effectively. In the given example, the primary voltage \(V_p\) is 240V from an outlet, and the secondary voltage \(V_s\) needed by the lamp is 120V. The relationship between these voltages helps determine how the transformer should be constructed.

The transformer utilizes the principle of electromagnetic induction. When an alternating current (AC) flows through the primary coil, it generates a magnetic field that induces a voltage in the secondary coil. Due to the transformer's design, this induced voltage is determined by the turns ratio of the coils.

If we apply the formula \(\frac{V_p}{V_s} = \frac{N_p}{N_s}\), substituting \(V_p=240\)V and \(V_s=120\)V, then simplifying \(\frac{240}{120} = 2\), we see that the primary coil voltage indeed is double the secondary coil voltage, necessitating twice as many turns in the primary coil compared to the secondary coil.

Let's delve into how a transformer operates. Transformers are pivotal devices in electrical engineering because they safely change voltage levels in AC circuits. They work based on the principle of magnetic induction.

Inside a transformer, two coils of wire are wound around a common iron core. One coil is the primary (connected to the input voltage), and the other is the secondary (connected to the output voltage). Electricity flowing through the primary coil generates a magnetic field, which, in turn, induces a voltage in the secondary coil. The efficiency of this induction process hinges on the coil turns ratio and the core's design.

Let's also remember essential transformer types such as step-up transformers, which increase voltage, and step-down transformers, which decrease voltage. In our example, the transformer steps down the voltage from 240V to 120V, which indicates a step-down transformer. This happens with the primary coil having more turns than the secondary coil, reflecting the need to reduce voltage for devices like a lava lamp.

Understanding transformer operation helps in safely adapting devices to varying voltage supplies across different regions.