Problem 25 - Applied Physics

Question

A mechanic is testing a transformer that increases voltage from \(11 \overline{0} \mathrm{~V}\) to \(30 \overline{0} 0 \mathrm{~V}\). If the primary coil has \(15 \overline{0}\) turns, how many turns are in the secondary coil?

Step-by-Step Solution

Answer

The secondary coil has approximately 4091 turns.

Step 1: Understanding the Problem

We have a transformer that changes voltage from 110 V to 3000 V. We need to find out how many turns are in the secondary coil knowing the primary coil has 150 turns.

Step 2: Using the Transformer Turns Ratio Formula

Transformers use the formula \( \frac{V_1}{V_2} = \frac{N_1}{N_2} \), where \( V_1 \) and \( V_2 \) are the voltages in the primary and secondary coil, respectively, and \( N_1 \) and \( N_2 \) are the number of turns in the primary and secondary coil respectively.

Step 3: Substitute Known Values into the Formula

Substitute the known values \( V_1 = 110 \), \( V_2 = 3000 \), and \( N_1 = 150 \) into the transformer formula: \[ \frac{110}{3000} = \frac{150}{N_2} \]

Step 4: Solve for the Unknown Turns \(N_2\)

Cross-multiply to solve for \(N_2\):\[ 110 \times N_2 = 150 \times 3000 \] Simplify:\[ N_2 = \frac{150 \times 3000}{110} \] Calculate:\[ N_2 = \frac{450000}{110} \approx 4091 \]

Step 5: Conclude the Number of Turns in the Secondary Coil

The secondary coil has about 4091 turns.

Key Concepts

Voltage Transformation

Voltage transformation is one of the primary functions of a transformer. A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. The process involves changing the voltage level as the electrical energy passes from the primary to the secondary coil. This change in voltage can be an increase or a decrease, depending on the design and purpose of the transformer. In our exercise, the transformer increases voltage from 110 V to 3000 V.

Voltage transformation can be represented by the formula \( \frac{V_1}{V_2} = \frac{N_1}{N_2} \), where:

• \( V_1 \) is the voltage in the primary coil.
• \( V_2 \) is the voltage in the secondary coil.
• \( N_1 \) is the number of turns in the primary coil.
• \( N_2 \) is the number of turns in the secondary coil.

By using this formula, we can understand how the number of turns in the coils affects the voltages and vice versa.

Primary Coil

The primary coil is where the input voltage is first applied in a transformer. It plays a crucial role in the initial step of voltage transformation. When an alternating current (AC) flows through the primary coil, it creates a varying magnetic field around the coil. This magnetic field is essential for inducing voltage in the secondary coil, which is part of how transformers function.

In this specific exercise, the primary coil is known to have 150 turns and receives a voltage of 110 V. These turns create the electromagnetic field needed to induce a higher voltage in the secondary coil. The number of turns in the primary coil, combined with the characteristics of the magnetic core, determines the strength and reach of the magnetic field.

Secondary Coil

The secondary coil in a transformer is where the voltage induced by the primary coil is converted into an output voltage. This process is driven by electromagnetic induction, which is a core principle of transformer operation. The secondary coil picks up the magnetic field created by the primary coil, transforming it into electrical energy at a different voltage level.

In this case, we need to determine how many turns the secondary coil should have to increase the voltage from 110 V to 3000 V. By using the transformer formula \( \frac{V_1}{V_2} = \frac{N_1}{N_2} \), we substitute the known values (\( V_1 = 110 \), \( V_2 = 3000 \), and \( N_1 = 150 \)) into the equation and solve for \( N_2 \). We find that the secondary coil should have approximately 4091 turns.

Electromagnetic Induction

Electromagnetic induction is the principle behind the operation of transformers. It is the process by which a changing magnetic field within a coil of wire induces voltage across the ends of the coil. This principle was first discovered by Michael Faraday in the 1830s and is foundational to the functioning of transformers.

The process works as follows:

• As an alternating current passes through the primary coil, it generates a changing magnetic field.
• This magnetic field passes through the transformer's core to the secondary coil.
• As the magnetic field changes, it induces a voltage in the secondary coil.

This induced voltage leads to the transformation of the voltage level between the primary and secondary coils, enabling the functionality of devices like transformers. The efficiency of electromagnetic induction in transformers is enhanced by the use of ferromagnetic cores, which concentrate the magnetic field and improve the coupling between the coils.