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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 principle of energy conservation because while it increases voltage, it decreases the current. Thus, the overall power (which is the product of current and voltage) remains the same, maintaining energy conservation.

Step by step solution

01

Understand Energy Conservation

The law of energy conservation states that energy can neither be created nor destroyed, only transformed from one form into another. This is a fundamental law of physics that applies to every process and system in the universe.
02

Understand Step-Up Transformers

A step-up transformer is used to increase the voltage of an electrical supply. This is done by having more turns of wire in the coil on the output (secondary) side than the input (primary) side. When alternating current flows into the primary coil, it generates a fluctuating magnetic field around the coil. This magnetic field induces a voltage in the secondary coil. Because there are more turns in the secondary coil, the voltage induced is larger than the incoming voltage.
03

Understand the Trade-Offs

The increase in voltage in a step-up transformer comes at the cost of a decrease in the current. This is due to the principle of energy conservation - the power (which is the product of current and voltage) must remain constant. So, if the voltage is increased by the transformer, the current must decrease to keep the power the same. This can be shown through the formula: P = VI. If V increases, to keep P constant, I (current) must decrease.

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Most popular questions from this chapter

A series \(R L C\) circuit with \(R=47 \Omega, L=250 \mathrm{mH},\) and \(C=4.0 \mu \mathrm{F}\) is connected across a sine-wave generator whose peak output voltage is independent of frequency. Find the frequency range over which the peak current will exceed half its value at resonance.

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