Un inductor de 20.0 mH se conecta a una salida eléctrica V estándar (Vr m=120 V ; f=60.0 Hz).

step 1 Okay in this question at 20 millie henry inductor is connected to standard outlet. Okay so induc

Un inductor de 20.0 mH se conecta a una salida eléctrica V...

Un inductor de $20.0 \mathrm{mH}$ se conecta a una salida eléctrica V estándar $\left(V_{r m}=120 \mathrm{~V} ; f=60.0 \mathrm{~Hz}\right)$. Determine la energía almacenada en el inductor a $t=(1 / 180) \mathrm{s}$, suponiendo que esta energia es cero a $t=0$.

Key Concepts

Inductance

Inductance is a property of an electrical component that quantifies its ability to store energy in a magnetic field when electrical current flows through it. It is measured in henries (H) and reflects the opposition a component offers to changes in current. This concept is central to understanding how circuits respond to time-varying signals.

Energy Storage in Inductive Components

The energy stored in an inductor is given by the expression U = 1/2 L I², where L is the inductance and I is the current through the inductor. This formula captures how energy is accumulated in the magnetic field during the passage of current and is fundamental in circuit analysis involving reactive elements.

AC Voltage Characteristics

AC (alternating current) voltage is characterized by a sinusoidal waveform that oscillates over time with a specific frequency and amplitude. Understanding the conversion between RMS (root mean square) values and peak voltages, as well as how the sinusoidal waveform influences the current in an inductive circuit, is key for analyzing energy storage in such systems.

Differential Equation for an Inductive Circuit

When an inductor is subjected to a time-varying voltage, the relationship V = L (dI/dt) governs the dynamic behavior of the current. Solving this differential equation by integrating the voltage function allows for determining how the current evolves over time, which is essential for calculating the energy stored in the inductor at any given moment.

Angular Frequency Calculation

Angular frequency (?) is related to the frequency (f) of an AC signal by the relation ? = 2?f. This parameter is crucial when working with sinusoidal functions in AC circuit analysis, as it facilitates the conversion of time domains into the frequency domain, aiding in the integration process and phase analysis.

Please give Ace some feedback