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Chapter 22: Problem 74

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 Transformer Basics

Transformers work on the principle of electromagnetic induction between two coils: primary and secondary. The voltage across these coils is governed by the turns ratio: \(\frac{V_s}{V_p} = \frac{N_s}{N_p}\), 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.
02

Identify Given Values

From the problem, we know that the primary voltage \(V_p\) is 120.0 V, the secondary voltage \(V_s\) is 4320 V, and the number of turns in the primary coil \(N_p\) is 21. We need to find the number of turns in the secondary coil \(N_s\).
03

Set Up the Transformer Equation

Using the formula \(\frac{V_s}{V_p} = \frac{N_s}{N_p}\), substitute the given values: \(\frac{4320}{120.0} = \frac{N_s}{21}\).
04

Solve for the Number of Turns in Secondary Coil

Rearrange the equation from Step 3 to solve for \(N_s\): \[ N_s = \frac{4320 \times 21}{120.0} \].
05

Calculate the Result

Perform the multiplication and division: \(N_s = \frac{90720}{120} = 756\). Thus, the secondary coil has 756 turns.

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Key Concepts

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

Electromagnetic Induction
Electromagnetic induction is the core principle that transformers rely on to function. It involves the generation of voltage across a conductor placed within a changing magnetic field. In the context of transformers, the primary coil generates a magnetic field when an AC voltage is applied. This alternating magnetic field then induces a voltage in the secondary coil.
  • Electromagnetic induction is why transformers can step up or step down voltage levels based on the arrangement of their coils.
  • The efficiency of energy transfer between the coils is dependent on the frequency of the AC voltage and the design of the transformer.
Understanding how this principle works allows us to comprehend the operation of many electrical devices which rely on transformers for their functionality.
Turns Ratio
The turns ratio is a fundamental concept in determining how a transformer changes voltage from input (primary) to output (secondary). It refers to the ratio of the number of windings in the secondary coil (\(N_s\)) to the number of windings in the primary coil (\(N_p\)).
  • Mathematically, the turns ratio is represented by \( \frac{N_s}{N_p} \).
  • This ratio directly dictates the ratio of secondary voltage (\(V_s\)) to primary voltage (\(V_p\)).
  • In essence, the turns ratio tells us how much the voltage will be transformed by the transformer.
In the insect zapper example, knowing the primary coil has 21 turns and calculating the necessary turns for the secondary coil allows us to determine how significantly the voltage will be stepped up.
Voltage Transformation
Voltage transformation in a transformer is the process of changing the electric potential (voltage) from one level to another using electromagnetic induction. This is vital in various applications, such as efficiently transmitting power over long distances or providing needed voltage levels for specific devices.
  • The voltage transformation follows the equation \( \frac{V_s}{V_p} = \frac{N_s}{N_p} \), ensuring the proportional relation between voltages and coil turns.
  • For a step-up transformer, as in the zapper example, the secondary voltage is higher than the primary voltage.
  • The relationship ensures energy conservation, with adjustments in voltage altering the current accordingly as per AC circuit principles.
In practical terms, understanding voltage transformation can help us solve problems involving transformers, ensuring devices like the insect zapper work smoothly and safely.

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Most popular questions from this chapter

ssm Two 0.68 -m-long conducting rods are rotating at the same speed in opposite directions, and both are perpendicular to a \(4.7-\mathrm{T}\) magnetic field. As the drawing shows, the ends of these rods come to within 1.0 \(\mathrm{mm}\) of each other as they rotate. Moreover, the fixed ends about which the rods are rotating are connected by a wire, so these ends are at the same electric potential. If a potential difference of \(4.5 \times 10^{3} \mathrm{V}\) is required to cause a \(1.0-\mathrm{mm}\) spark in air, what is the angular speed (in rad/s) of the rods when a spark jumps across the gap?

A planar coil of wire has a single turn. The normal to this coil is parallel to a uniform and constant (in time) magnetic field of 1.7 \(\mathrm{T}\) . An emf that has a magnitude of 2.6 \(\mathrm{V}\) is induced in this coil because the coil's area \(A\) is shrinking. What is the magnitude of \(\Delta A / \Delta t,\) which is the rate (in \(\mathrm{m}^{2} / \mathrm{s} )\) at which the area changes?

A flat coil of wire has an area \(A, N\) turns, and a resistance \(R .\) It is situated in a magnetic field, such that the normal to the coil is parallel to the magnetic field. The coil is then rotated through an angle of \(90^{\circ},\) so that the normal becomes perpendicular to the magnetic field. The coil has an area of \(1.5 \times 10^{-3} \mathrm{m}^{2}, 50\) turns, and a resistance of 140\(\Omega .\) During the time while it is rotating, a charge of \(8.5 \times 10^{-5}\) C flows in the coil. What is the magnitude of the magnetic field?

A 120.0 -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 \(\mathrm{A}\) ?

The magnetic flux that passes through one turn of a 12 -turn coil of wire changes to 4.0 \(\mathrm{from} 9.0 \mathrm{Wb}\) in a time of 0.050 \(\mathrm{s}\) . The average induced current in the coil is 230 \(\mathrm{A}\) . What is the resistance of the wire?
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