Calculate the current in the inductor shown in Fig. P8.9 if...

Calculate the current in the inductor shown in Fig. P8.9 if the voltage input is
(a) $v_{1}(t)=10 \cos \left(377 t+45^{\circ}\right) \mathrm{V}$
(b) $v_{2}(t)=5 \sin \left(377 t-90^{\circ}\right) \mathrm{V}$
Give the answers in both the time and frequency domains.

Key Concepts

Sinusoidal Steady-State Analysis

Sinusoidal steady-state analysis is employed when analyzing circuits driven by sinusoidal sources that have been operating for a long time. In this state, all currents and voltages in the circuit have settled into sinusoidal waveforms with constant amplitudes and phases, and analysis can be efficiently performed using phasors.

Impedance in AC Circuits

Impedance is the frequency-domain equivalent of resistance in AC circuits and accounts for both resistive and reactive elements. For an inductor, the impedance is expressed as j?L, where ? is the angular frequency and L is the inductance. This concept is key to analyzing how inductors impede the flow of alternating current.

Phasor Representation

Phasor representation involves converting sinusoidal functions in the time domain into complex numbers in the frequency domain. This simplifies the analysis of AC circuits by turning differential equations into algebraic equations, allowing for easier handling of amplitude and phase information.

Inductor Voltage-Current Relationship

This concept explains the fundamental time-domain relationship between the voltage across an inductor and the current through it, typically given by v(t) = L(di(t)/dt). Understanding this relationship is crucial for determining the current response of an inductor when subjected to a given voltage waveform.

Transcript

Please give Ace some feedback