Problem 47 - Physics for Scientists and Engineers with Modern Physics

Question

(I) Neon signs require \(12 \mathrm{kV}\) for their operation. To operate from a \(240-\mathrm{V}\) line, what must be the ratio of secondary to primary turns of the transformer? What would the voltage output be if the transformer were connected backward?

Step-by-Step Solution

Answer

The turns ratio is 50:1, and the backward connection outputs 4.8 V.

Step 1: Understand the Problem

We have a neon sign requiring a voltage of \(12 \text{kV}\) to operate and a power source providing \(240 \text{V}\). We need to find the turns ratio for a transformer connected to increase the voltage from \(240 \text{V}\) to \(12 \text{kV}\).

Step 2: Formula for Turns Ratio

The turns ratio \(n\) of a transformer is given by \(n = \frac{V_{secondary}}{V_{primary}}\). Here, \(V_{secondary} = 12 \text{kV} = 12000 \text{V}\) and \(V_{primary} = 240 \text{V}\).

Step 3: Calculate the Turns Ratio

Using the formula, the turns ratio is \(n = \frac{12000}{240} = 50\). Thus, the transformer should have 50 secondary turns for every primary turn.

Step 4: Connect the Transformer Backward

If the transformer is connected backward, the turns ratio is inverted. Thus, the new primary voltage would be \(240 \text{V} \times \frac{1}{50} = 4.8 \text{V}\). This means that feeding 240 V to the secondary results in a primary voltage of 4.8 V.

Key Concepts

Neon Signs

Neon signs are vibrant, eye-catching displays that have been around for over a century. These signs rely on the electrical excitation of gas, primarily neon or argon, to produce their iconic glow. When high voltage is applied across the terminals of a sealed glass tube filled with this gas, the atoms within the gas become excited and emit light.

The operation of neon signs depends heavily on voltage, specifically a high voltage of about 12,000 volts (12 kV) is required for them to shine brightly. This is much higher than the standard household voltage, which is typically around 120 V to 240 V. To bridge this gap and safely power neon signs, transformers are used. These devices adjust the voltage to a suitable level, making it possible for them to be used in various commercial and decorative contexts.

Voltage Transformation

Voltage transformation is a fundamental concept in electrical engineering, playing a critical role in the operation of devices from household gadgets to industrial machinery. A transformer is a key component in this procedure. It alters the voltage of electric power as it passes through a pair of wire coils, known as the primary and secondary windings.

The transformation process is governed by the turns ratio, which is determined by the number of coils in the primary winding compared to the secondary. For a neon sign, with a primary voltage of 240 V and a secondary voltage requirement of 12 kV, the turns ratio is calculated to be 50. This means that for every single loop of wire on the primary winding, there are 50 loops on the secondary winding. As a result, this increases the voltage required to power the neon sign.

If the transformer is connected backward, the turns ratio effectively becomes inverted. This dramatically reduces the output voltage, leading to a scenario where 240 V given at the secondary would only produce about 4.8 V at the primary.

Electrical Engineering

Electrical engineering is the field that deals with the study and application of electricity, electronics, and electromagnetism. From power generation and distribution to intricate device circuitry, it encompasses a wide range of topics and technologies.

Transformers, like those used for neon signs, are a vital part of this discipline. They allow for the efficient transmission and utilization of electrical power by adjusting voltage levels to suit various applications.

In the context of neon signs, understanding the principles of electrical engineering is essential for designing systems that can safely and effectively manage high voltages. It involves the mastery of concepts such as the turns ratio and transformer efficiency. These principles not only help in powering neon signs but are also crucial in broader electrical systems, ensuring reliability and safety across the board.

• The primary function of an electrical engineer is to ensure that electrical systems operate smoothly and efficiently.
• Transformers are one among many tools used to achieve the desired electrical output.
• Knowledge of voltage transformation and electrical circuits is essential for tackling real-world engineering challenges.