Problem 16 - Applied Physics

Question

A transformer has \(20.0\) turns in the primary coil and \(22 \overline{0} 0\) turns in the secondary. If the primary voltage is \(12.0 \mathrm{~V}\), what is the secondary voltage?

Step-by-Step Solution

Answer

The secondary voltage is 1320.0 V.

Step 1: Identify Known Values

In this transformer problem, we know the primary coil has 20 turns, the secondary coil has 2200 turns, and the primary voltage is 12.0 V.

Step 2: Use the Transformer Voltage Equation

We use the relationship between the primary and secondary voltages and the number of turns: \[ \frac{V_s}{V_p} = \frac{N_s}{N_p} \] where \(V_s\) and \(V_p\) are the secondary and primary voltages, and \(N_s\) and \(N_p\) are the number of turns in the secondary and primary coils, respectively.

Step 3: Substitute the Known Values into the Equation

Substituting the given values into the equation, we have: \[ \frac{V_s}{12.0} = \frac{2200}{20} \].

Step 4: Solve for the Secondary Voltage

Now, solve for \(V_s\) by multiplying both sides of the equation by 12.0: \[ V_s = 12.0 \times \frac{2200}{20} = 12.0 \times 110 \].

Step 5: Calculate the Result

Perform the multiplication to find \(V_s\): \[ V_s = 1320.0 \text{ V} \]. Thus, the secondary voltage is 1320.0 V.

Key Concepts

Primary and Secondary Coils

In a transformer, there are two coils of wire called the primary coil and the secondary coil. The primary coil is connected to the input voltage source, such as an electrical outlet, and it is responsible for receiving the initial electricity. Meanwhile, the secondary coil is where the transformed voltage is either stepped up or stepped down for use in the intended appliance or circuit.
Differences in the number of turns between the primary and secondary coils play a crucial role in determining how the voltage is altered. The primary coil acts as the starting point for electricity, and the secondary coil usually delivers this transformed electricity to consumers. Together, these coils work to either increase or decrease voltage levels as required. Transformers are essential in power distribution to ensure electrical equipment operates correctly.

Turns Ratio

The turns ratio of a transformer is a vital concept that reflects the proportion of the number of turns in the secondary coil to that in the primary coil. It is written as:

• Turns ratio = \( \frac{N_s}{N_p} \)
• \(N_s\) is the number of turns in the secondary coil
• \(N_p\) is the number of turns in the primary coil

The turns ratio consequently determines how much the voltage is increased or decreased. If the turns ratio is greater than one, the transformer increases the voltage, thus stepping it up. Conversely, if less than one, the transformer decreases the voltage, stepping it down. This ability to transform voltage levels makes transformers immensely beneficial in both residential and industrial settings.

Transformer Equations

Transformers use a set of equations that relate the transformer’s characteristics and behaviors in terms of primary and secondary voltages and turns. The foundational formula connecting these variables is:

• \( \frac{V_s}{V_p} = \frac{N_s}{N_p} \)

Here, \(V_s\) and \(V_p\) are the voltages in the secondary and primary coils, respectively. By rearranging this equation, one can find unknown values, such as voltage or coil turns, when other variables are provided. These transformer equations are crucial for electrical engineers and others in applied physics because they efficiently describe how transformers work, simplifying the process of designing and troubleshooting electrical systems.

Voltage Transformation

Voltage transformation is at the heart of what transformers do. This process takes an input voltage (primary voltage) and changes it to the desired output voltage (secondary voltage).
In tasks of voltage transformation, understanding the turns ratio allows one to predict how the input voltage will be adapted according to the equation

• Secondary voltage \(V_s = V_p \times \frac{N_s}{N_p} \)

By using this formula, one can easily calculate the new voltage, which is essential for ensuring devices receive the correct voltage needed for their operation. Without proper voltage transformation, electrical devices could malfunction or become damaged, emphasizing why this concept is crucial.

Applied Physics Problems

Working with transformers and their related calculations can be part of broader applied physics problems. These practical problems often arise in real-world applications such as engineering, where processes involve transforming voltages to suit various needs.
Understanding and solving applied physics problems requires a solid grasp of key concepts like primary and secondary coils, turns ratios, and transformer equations. Through these concepts, one can interpret and solve problems that might include designing electrical grids, ensuring household appliances receive the correct voltage, or even creating efficient power systems for industrial settings. With a sturdy foundation in these principles, tackling such applied physics problems becomes more approachable and manageable for students and professionals alike.