/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 74 In some places, insect "zappers,... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

In some places, insect "zappers," with their blue lights, are a familiar sight on a summer's night. These devices use a high voltage to electrocute insects. One such device uses an ac voltage of \(4320 \mathrm{V},\) which is obtained from a standard \(120.0-\mathrm{V}\) outlet by means of a transformer. If the primary coil has 21 turns, how many turns are in the secondary coil?

Short Answer

Expert verified
The secondary coil has 756 turns.

Step by step solution

01

Understand the Problem

We need to find the number of turns in the secondary coil of a transformer that steps up the voltage from an initial 120.0 V to 4320 V. The primary coil has 21 turns.
02

Identify the Transformer Equation

The equation that relates the number of turns in the coils of a transformer to the voltages across them is \( \frac{N_s}{N_p} = \frac{V_s}{V_p} \), where \(N_s\) is the number of turns in the secondary coil, \(N_p\) is the number of turns in the primary coil, \(V_s\) is the secondary voltage, and \(V_p\) is the primary voltage.
03

Substitute Known Values

Using the equation \( \frac{N_s}{N_p} = \frac{V_s}{V_p} \), substitute \( N_p = 21 \), \( V_s = 4320 \) V, and \( V_p = 120 \) V. Hence, the equation becomes \( \frac{N_s}{21} = \frac{4320}{120} \).
04

Solve for the Secondary Turns

Calculate the right side of the equation: \( \frac{4320}{120} = 36 \). Thus, we have \( \frac{N_s}{21} = 36 \). Solving for \(N_s\), we multiply both sides of the equation by 21, obtaining \(N_s = 21 \times 36 = 756\).
05

Verification

Verify the calculated number of turns by checking the units and making basic calculations again if necessary, to ensure the answer makes sense.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

AC voltage transformation
AC voltage transformation is a process where alternating current (AC) voltage is changed from one level to another using a device called a transformer. This is essential in electrical systems to either step up (increase) or step down (decrease) voltage according to the needs of a specific application.
For example, in the situation with the insect zapper, a higher voltage is needed to effectively catch insects. The transformer takes the standard 120 V from an outlet and transforms it to 4320 V, suitable for the zapper's operation.
The transformer does all this by using the principles of electromagnetic induction, which allows it to modify voltage levels without direct electrical connection between input and output. Understanding how AC voltage transformation works is crucial for designing efficient electrical devices.
step-up transformer
A step-up transformer is a type of transformer that increases or "steps up" the voltage from a lower level to a higher level. It is primarily used when high voltage is required for efficient device operation or to transmit electric power over long distances, reducing energy loss.
In the insect zapper scenario, the step-up transformer converts the lower 120 V AC from the outlet to the much higher voltage of 4320 V, necessary for generating a strong electric field to electrocute insects.
  • The primary coil has fewer turns compared to the secondary coil.
  • This is the opposite of a step-down transformer, which reduces voltage.
By increasing the voltage, less current is required to deliver the same amount of power, which makes step-up transformers vital in both small devices and large-scale power distribution systems.
secondary coil turns
The number of turns in a secondary coil of a transformer is a key factor that influences the output voltage. In our example, the insect zapper's transformer has 756 turns on its secondary coil.
The relationship between the number of turns in the primary and secondary coils and their respective voltages is defined by the transformer equation:\[ \frac{N_s}{N_p} = \frac{V_s}{V_p} \]where \(N_s\) is the number of turns in the secondary coil, and \(V_s\) is the secondary voltage. Knowing the turns in the primary coil and the respective voltages allows us to calculate \(N_s\).
Achieving precise voltage levels through accurate calculation of secondary coil turns is crucial for the transformer's efficiency and the device's safety. This calculation ensures the device receives the appropriate voltage needed for optimal performance.
electromagnetic induction
Electromagnetic induction is the fundamental principle behind the operation of transformers. It was discovered by Michael Faraday and involves generating an electric current in a conductor by changing the magnetic field nearby.
In transformers, electromagnetic induction occurs as follows:
  • An alternating current in the primary coil creates a changing magnetic field.
  • This fluctuating magnetic field induces an electromotive force (EMF) in the secondary coil.
  • The induced EMF causes an electrical current to flow, enabling the transformation of voltage levels.
The efficiency and effectiveness of a transformer heavily rely on the principles of electromagnetic induction, which allow for the smooth and efficient transfer of energy from one circuit to another, with or without changing voltage levels. Understanding this concept is key to grasp how transformers such as the one in the insect zapper can step up voltage while maintaining safety and reliability.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The rechargeable batteries for a laptop computer need a much smaller voltage than what a wall socket provides. Therefore, a transformer is plugged into the wall socket and produces the necessary voltage for charging the batteries. The batteries are rated at \(9.0 \mathrm{V},\) and a current of \(225 \mathrm{mA}\) is used to charge them. The wall socket provides a voltage of \(120 \mathrm{V}\). (a) Determine the turns ratio of the transformer. (b) What is the current coming from the wall socket? (c) Find the average power delivered by the wall socket and the average power sent to the batteries.

A flat circular coil with 105 turns, a radius of \(4.00 \times 10^{-2} \mathrm{m},\) and a resistance of \(0.480 \Omega\) is exposed to an external magnetic field that is directed perpendicular to the plane of the coil. The magnitude of the external magnetic field is changing at a rate of \(\Delta B / \Delta t=0.783 \mathrm{T} / \mathrm{s},\) thereby inducing a current in the coil. Find the magnitude of the magnetic field at the center of the coil that is produced by the induced current.

A \(120.0-\mathrm{V}\) motor draws a current of \(7.00 \mathrm{A}\) when running at normal speed. The resistance of the armature wire is \(0.720 \Omega .\) (a) Determine the back emf generated by the motor. (b) What is the current at the instant when the motor is just turned on and has not begun to rotate? (c) What series resistance must be added to limit the starting current to \(15.0 \mathrm{A} ?\)

A Generator Bike. You and your team are designing a generator using a stationary bike to rotate a coil in a uniform magnetic field. The gearing is set up so that the coil rotates 60 times for one complete rotation of the bike pedals. Therefore, one revolution of the pedals per second results in a \(60-\mathrm{Hz}\) alternating current in the coil. The circular coil has 350 turns and a diameter of \(15.0 \mathrm{cm},\) and its axis of rotation is along its diameter. (a) If a uniform magnetic field is oriented perpendicular to the coil's axis of rotation and has a magnitude of \(B=0.225 \mathrm{T}\), what is the peak emf produced by the generator bike? (b) What is the rms emf? (c) To what magnitude should you reduce the field if you want the rms emf to be 110 VAC? (d) Instead of reducing the field, you could use a step-down transformer to reduce the rms emf to 110 VAC. What should be the ratio of primary to secondary turns of the transformer coils?

A long solenoid of length \(8.0 \times 10^{-2} \mathrm{m}\) and cross-sectional area \(5.0 \times 10^{-5} \mathrm{m}^{2}\) contains 6500 turns per meter of length. Determine the emf induced in the solenoid when the current in the solenoid changes from 0 to 1.5 A during the time interval from 0 to 0.20 s.

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.