Question

Si el inductor de la figura $17-32$ se reemplaza con un capacitor de $40 \mu \mathrm{~F}$ y la frecuencia de la fuente es 60 Hz , ¿cuánto vale $Q_C$ ?

    Si el inductor de la figura $17-32$ se reemplaza con un capacitor de $40 \mu \mathrm{~F}$ y la frecuencia de la fuente es 60 Hz , ¿cuánto vale $Q_C$ ?
Análisis de circuitos. Teoría y práctica.
Análisis de circuitos. Teoría y práctica.
Allan H. Robbins,… 4th Edition
Chapter 17, Problem 5 ↓

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La carga \( Q_C \) en un capacitor se puede calcular usando la fĂłrmula: \[ Q_C = C \cdot V \] donde \( C \) es la capacitancia en faradios y \( V \) es el voltaje en voltios.  Show more…

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Si el inductor de la figura $17-32$ se reemplaza con un capacitor de $40 \mu \mathrm{~F}$ y la frecuencia de la fuente es 60 Hz , ¿cuánto vale $Q_C$ ?
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Key Concepts

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AC Frequency
The frequency of an AC signal is a fundamental parameter that affects the behavior of reactive components like capacitors and inductors. It determines the rate at which the alternating current oscillates and directly influences the capacitive reactance. As frequency increases, the reactance of a capacitor decreases, impacting the circuit's overall impedance and the calculation of reactive power. Thus, frequency is a critical factor in AC circuit analysis and design.
Capacitive Reactance
Capacitive reactance is the opposition that a capacitor presents to the flow of alternating current, and it depends inversely on both the frequency of the AC source and the capacitance value. It is calculated using the formula Xc = 1/(2?fC), where f is the frequency of the source and C is the capacitance. This concept is essential in AC circuit analysis because it determines how the capacitor will influence the circuit's overall impedance.
Reactive Power in AC Circuits
Reactive power refers to the portion of power in an AC circuit that oscillates between the source and reactive components, such as capacitors or inductors, without being dissipated as heat. In the case of capacitors, reactive power can be computed using formulas that involve the voltage across the capacitor and its reactance, typically expressed as Q = V^2/Xc. Understanding reactive power is important for designing and analyzing circuits to ensure proper voltage regulation and efficient energy transfer.

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The charge q in an electrical circuit is given by d^2q/dt^2 + R/L * dq/dt + 1/LC * q = E. If inductance L is 0.25 H, capacitance C is 40 x 10^-6 F, resistance R is 200 Ω, and E is 240 V, solve the equation for q given the boundary conditions that when t = 0, q = 0, and dq/dt = 35.

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