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Chapter 28: Problem 13

A step-up transformer increases voltage, or energy per unit charge. Why doesn't this violate energy conservation?

Short Answer

Expert verified
A step-up transformer doesn't violate the law of conservation of energy because although it increases voltage, it decreases the current such that the overall power (which is the product of voltage and current) remains constant. Therefore, no energy is created or lost, preserving energy conservation.

Step by step solution

01

Understanding How a Transformer Works

A transformer is a device that either increases or decreases the voltage of an alternating current. In the case of a step-up transformer, it increases the voltage. It does so through electromagnetic induction, where the input current to the primary coil creates a magnetic field which then induces a voltage in the secondary coil.
02

Understanding the Law of Conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed, but only changed from one form into another or transferred from one body to another. So even if a transformer increases the voltage, it must do so without creating any new energy.
03

Explanation of the Energy Conservation in a Transformer

While a step-up transformer does indeed increase the voltage, or energy per unit charge, it also reduces the current. This is due to the fact that the power (which is the product of voltage and current, \(P = IV\)), remains constant in an ideal transformer. Therefore, as the voltage increases, the current must decrease to keep the power the same. This is why a step-up transformer doesn't violate energy conservation - because the total energy remains the same, it's just distributed in a different manner.

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Most popular questions from this chapter

Much of Europe uses AC power at \(230 \mathrm{V}\) rms and \(50 \mathrm{Hz}\). Express this AC voltage in the form of Equation \(28.3,\) taking \(\phi_{V}=0\)

Find the impedance at \(10 \mathrm{kHz}\) of a circuit consisting of a \(1.5-\mathrm{k} \Omega\) resistor, \(5.0-\mu \mathrm{F}\) capacitor, and \(50-\mathrm{mH}\) inductor in series.

A \(50-\mathrm{mH}\) inductor is connected across a \(10-\mathrm{V}\) rms AC generator, and a 2.0 -mA rms current flows. What's the generator frequency?

A triangle wave swings linearly between voltages \(-V_{\mathrm{p}}\) and \(+V_{\mathrm{p}}\) Show that the rms voltage of a triangle wave is \(V_{\mathrm{p}} / \sqrt{3}\)

A 15 - \(\mu\) F capacitor carries \(1.4 \mathrm{A}\) rms. What's its minimum safe voltage rating if the frequency is (a) \(60 \mathrm{Hz}\) and (b) \(1.0 \mathrm{kHz} ?\)
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