Electricity is distributed from electrical substations to neighborhoods at 15,000 V. This is a 60 Hz oscillating (AC) voltage. Neighborhood transformers, seen on utility poles, step this voltage down to the 120 V that is delivered to your house. a. How many turns does the primary coil on the transformer have if the secondary coil has 100 turns?

Verified step by step guidance

1. Understand the problem: This is a transformer problem, which operates on the principle of electromagnetic induction. The relationship between the number of turns in the primary and secondary coils and their respective voltages is given 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 in the primary and secondary coils, respectively.
2. Identify the known values: From the problem, the primary voltage is $15,000$ V, the secondary voltage is $120$ V, and the number of turns in the secondary coil is $100$ turns.
3. Rearrange the transformer equation to solve for the number of turns in the primary coil: $N_p=\frac{V_p}{V_s}\cdot N_s$. This equation allows us to calculate the number of turns in the primary coil based on the given values.
4. Substitute the known values into the equation: $N_p=\frac{\mathrm{15,000}}{120}\cdot 100$. Perform the division and multiplication to find the number of turns in the primary coil.
5. Interpret the result: The calculated value of $N_p$ represents the number of turns in the primary coil of the transformer. This value should be significantly larger than the number of turns in the secondary coil, as the primary voltage is much higher than the secondary voltage.

Key Concepts

Transformer Basics

A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It consists of primary and secondary coils, where the primary coil receives the input voltage and the secondary coil delivers the output voltage. The voltage change between the coils is proportional to the ratio of the number of turns in each coil.

Turns Ratio

The turns ratio of a transformer is the ratio of the number of turns in the primary coil to the number of turns in the secondary coil. This ratio determines how the voltage is transformed; if the primary coil has more turns than the secondary, the voltage is stepped down, while if it has fewer, the voltage is stepped up. The relationship can be expressed as Vp/Vs = Np/Ns, where V is voltage and N is the number of turns.

AC Voltage Characteristics

Alternating current (AC) voltage is characterized by its periodic oscillation, typically described by its frequency, measured in hertz (Hz). In this case, the 60 Hz frequency indicates that the voltage alternates direction 60 times per second. This oscillation is crucial for the operation of transformers, as they rely on changing magnetic fields to induce voltage in the secondary coil.