Transformers: Videos & Practice Problems

Transformers utilize electromagnetic induction to convert high voltages to lower voltages, essential for safe household power delivery. According to Faraday's law, a changing magnetic field in one coil induces an electromotive force (emf) in a nearby coil. The voltage ratio between input and output coils is determined by the turns ratio: VV = NN. For example, to reduce 120 volts to 15 volts, a transformer with a 50-turn coil can require a second coil with as few as 6.25 turns, demonstrating the efficiency of transformers in electrical circuits.

Transformers

Transformers are essential devices that utilize the principle of electromagnetic induction to adjust voltage levels for efficient power delivery from generators to homes. In North America, the standard voltage delivered to households is 120 volts, which can be too high for sensitive electronics. Therefore, transformers are used to step down this voltage to safer levels.

The operation of a transformer is based on Faraday's law of electromagnetic induction, which states that a changing magnetic field can induce an electromotive force (emf) in a nearby coil. A typical transformer consists of two solenoids (coils) placed close to each other, each with a different number of turns. The relationship between the input voltage (V₁) and output voltage (V₂) is governed by the equation:

\[ \frac{V_2}{V_1} = \frac{N_2}{N_1} \]

where N₁ is the number of turns in the input solenoid and N₂ is the number of turns in the output solenoid. This equation allows us to determine how the voltages relate to the number of turns in each solenoid.

For example, if we want to design a transformer that reduces 120 volts to 15 volts, we can set up the equation:

\[ \frac{15}{120} = \frac{N_2}{50} \]

Solving this gives us a ratio of 1/8. We can rearrange the equation to find N₂ in two ways: either as N₂ = 8 × N₁ or N₁ = N₂ / 8. Plugging in N₁ = 50 turns, we find:

1. If N₁ is the output solenoid, then N₂ = 6.25 turns.

2. If N₁ is the input solenoid, then N₂ = 400 turns.

Clearly, the configuration that requires the least number of turns for the second solenoid is when it has 6.25 turns, making it the input solenoid. This demonstrates how transformers can be designed to efficiently convert high voltages to lower, safer levels for household use.

Example

In this problem, we are tasked with designing a transformer that reduces the voltage from a standard North American outlet of 120 volts to a safer 15 volts. To achieve this, we need to determine the number of turns in a second solenoid, given that we already have a first solenoid with 50 turns.

The relationship between the voltages and the number of turns in a transformer is defined by the equation:

\[ \frac{V_2}{V_1} = \frac{N_2}{N_1} \]

Here, \(V_1\) is the input voltage (120 volts), \(V_2\) is the output voltage (15 volts), \(N_1\) is the number of turns in the first solenoid, and \(N_2\) is the number of turns in the second solenoid. Substituting the known values into the equation gives us:

\[ \frac{15}{120} = \frac{N_2}{50} \]

This simplifies to:

\[ \frac{1}{8} = \frac{N_2}{50} \]

From this, we can derive that:

\[ N_2 = \frac{50}{8} = 6.25 \text{ turns} \]

However, we also need to consider the alternative scenario where \(N_2\) is 50 turns. In this case, we can rearrange the equation to find \(N_1\):

\[ \frac{1}{8} = \frac{50}{N_1} \]

This leads to:

\[ N_1 = 50 \times 8 = 400 \text{ turns} \]

Comparing the two outcomes, we find that 6.25 turns is significantly fewer than 400 turns. Therefore, the optimal solution is to have the first solenoid with 50 turns, resulting in the second solenoid needing only 6.25 turns to achieve the desired voltage transformation.

This analysis highlights the importance of understanding the transformer equations and the relationship between voltage and the number of turns in solenoids, which is crucial for designing efficient electrical systems.

An outlet in North America outputs electricity at 120 V, but a typical laptop needs to operate at around 20 V. In order to do so, a transformer is placed in a laptop's power supply. If the coil in the circuit connected to the laptop has 20 turns, how many turns must the coil in the circuit with the outlet have?

• A. 3 turns
• B. 6 turns
• C. 20 turns
• D. 120 turns

Answer: (D)

Here’s what students ask on this topic:

What is the principle of operation of a transformer?

A transformer operates on the principle of electromagnetic induction, as described by Faraday's law. When an alternating current (AC) flows through the primary coil, it creates a changing magnetic field. This changing magnetic field induces an electromotive force (emf) in the secondary coil. The voltage induced in the secondary coil depends on the ratio of the number of turns in the primary coil to the number of turns in the secondary coil, given by the equation:

$\frac{V_2}{V_1}=\frac{N_2}{N_1}$

How do you calculate the number of turns needed in a transformer coil?

To calculate the number of turns needed in a transformer coil, you use the turns ratio formula:

$\frac{V_2}{V_1}=\frac{N_2}{N_1}$

Here, $V_1$ is the input voltage, $V_2$ is the output voltage, $N_1$ is the number of turns in the primary coil, and $N_2$ is the number of turns in the secondary coil. Rearrange the formula to solve for the unknown number of turns.

Why are transformers important in power distribution?

Transformers are crucial in power distribution because they allow the efficient transmission of electrical power over long distances. High voltages are used to minimize energy loss due to resistance in the transmission lines. Transformers step up the voltage at the power generation site and step it down at the distribution end to safe levels for household and industrial use. This process ensures that electrical power is delivered efficiently and safely to consumers.

What is the difference between a step-up and a step-down transformer?

A step-up transformer increases the voltage from the primary coil to the secondary coil. It has more turns in the secondary coil than in the primary coil. Conversely, a step-down transformer decreases the voltage from the primary coil to the secondary coil, having fewer turns in the secondary coil than in the primary coil. The turns ratio determines whether the transformer is step-up or step-down.

How does Faraday's law apply to transformers?

Faraday's law of electromagnetic induction states that a changing magnetic field within a coil of wire induces an electromotive force (emf) in the coil. In transformers, an alternating current in the primary coil creates a changing magnetic field, which induces an emf in the secondary coil. The induced voltage in the secondary coil is proportional to the rate of change of the magnetic flux and the number of turns in the coil, as described by Faraday's law.