Treat the solenoid and coil of Solved Problem 29.2 as a...

Treat the solenoid and coil of Solved Problem 29.2 as a transformer. a) Find the root-mean-square voltage in the coil if the solenoid has a rootmean-square voltage of $120 \mathrm{~V}$ and a frequency of $60 . \mathrm{Hz} .$ The length of the solenoid is $12.0 \mathrm{~cm}$. b) What is the voltage in the coil if the frequency is $0 \mathrm{~Hz}$ (DC current)?

Treat the solenoid and coil of Solved Problem 29.2 as a transformer.
a) Find the root-mean-square voltage in the coil if the solenoid has a rootmean-square voltage of $120 \mathrm{~V}$ and a frequency of $60 . \mathrm{Hz} .$ The length of the solenoid is $12.0 \mathrm{~cm}$.
b) What is the voltage in the coil if the frequency is $0 \mathrm{~Hz}$ (DC current)?

Key Concepts

Alternating Current (AC) versus Direct Current (DC) in Induction

In the context of electromagnetic induction, AC and DC behave very differently. Alternating current produces a continuously changing magnetic field, which, according to Faraday's Law, induces an emf in nearby coils. In contrast, direct current (DC) produces a steady magnetic field, resulting in no change in magnetic flux over time and therefore failing to induce any emf once the current has reached a constant level. This distinction is crucial for understanding the operation of devices like transformers that rely on AC to function.

Transformer

A transformer is an electrical device that transfers energy between two or more circuits through electromagnetic induction. It consists of at least two coils (a primary and a secondary) that are magnetically coupled. When an alternating current flows through the primary coil, it produces a time-varying magnetic field which, in turn, induces an electromotive force (emf) in the secondary coil. The operating principle of a transformer is rooted in electromagnetic induction and is critical for adjusting voltage levels in power systems.

Faraday's Law of Electromagnetic Induction

Faraday's Law states that a changing magnetic flux through a circuit induces an electromotive force (emf) in the circuit. The induced emf is proportional to the rate of change of the magnetic flux. This principle explains how transformers, as well as many other electrical devices such as generators and induction coils, function by converting changing magnetic fields into electrical energy.

Root-Mean-Square (RMS) Voltage

The root-mean-square (rms) voltage is a statistical measure of the effective or equivalent direct current (DC) voltage of an alternating current (AC) signal. It represents the value of a constant voltage that would deliver the same power to a resistive load as the time-varying AC voltage. This concept is key in AC circuit analysis and power calculations since AC voltages vary over time.

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