When the Current Is Maximum An ac generator has emf ℰ= ℰ^max sinω^dr t, with ℰ^max=25.0 V and ω

step 1 Hi, here in this given problem emf of the AC generator that is E is equal to em, em means maximu

When the Current Is Maximum An ac generator has emf ℰ= ℰ^max...

When the Current Is Maximum An ac generator has emf $\mathscr{E}=$ $\mathscr{E}^{\max } \sin \omega^{\mathrm{dr}} t$, with $\mathscr{E}^{\max }=25.0 \mathrm{~V}$ and $\omega^{\mathrm{dr}}=377 \mathrm{rad} / \mathrm{s} .$ It is con- nected to a $12.7 \mathrm{H}$ inductor. (a) What is the maximum value of the current? (b) When the current is a maximum, what is the emf of the generator? (c) When the emf of the generator is $-12.5 \mathrm{~V}$ and increasing in magnitude, what is the current?

When the Current Is Maximum An ac generator has emf $\mathscr{E}=$ $\mathscr{E}^{\max } \sin \omega^{\mathrm{dr}} t$, with $\mathscr{E}^{\max }=25.0 \mathrm{~V}$ and $\omega^{\mathrm{dr}}=377 \mathrm{rad} / \mathrm{s} .$ It is con-
nected to a $12.7 \mathrm{H}$ inductor. (a) What is the maximum value of the current? (b) When the current is a maximum, what is the emf of the generator? (c) When the emf of the generator is $-12.5 \mathrm{~V}$ and increasing in magnitude, what is the current?

Key Concepts

Phase Relationships in Inductive Circuits

In an ideal inductive AC circuit, the voltage and current are out of phase; specifically, the voltage leads the current by 90 degrees. This phase difference is crucial when analyzing conditions such as maximum current or maximum voltage, since the peaks of the sinusoidal functions occur at different times.

Inductive Reactance

Inductive reactance is the effective opposition that an inductor presents to a changing current and is calculated as X_L = ?L, where ? is the angular frequency. This concept combines inductance with AC frequency, determining the amplitude relationship between the voltage across and the current through the inductor.

Sinusoidal AC Waveforms

Alternating current generators produce voltages that vary sinusoidally with time, characterized by a maximum amplitude, angular frequency, and phase. These sinusoidal functions are fundamental in understanding AC circuits as they indicate how voltage and current change cyclically over time.

Inductance and Its Role in AC Circuits

Inductance is a property of electrical circuits, particularly with coils or inductors, which opposes changes in current. In AC circuits, the inductance L causes the voltage across the inductor to depend on the time derivative of the current, expressed as V = L(dI/dt). This relationship is central to analyzing how current evolves in response to a time-varying voltage.

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