AC Circuit Analysis: Calculating Reactance and Impedance
What is the reactance of a capacitor in an AC circuit?
The reactance of a capacitor in an AC circuit is calculated. Using this, the total impedance of the series circuit is worked out. From this, the current in the AC circuit is calculated to be approximately 0.111 A.
Answer:
The reactance (Xc) of a capacitor in an AC circuit can be calculated using the formula: Xc = 1/(2πfC), where f is the frequency and C is the capacitance. Substituting given values, Xc = 1/(2π(60)(2.5 x 10^-6)) = 1061 Ohms. Next, the total impedance (Z) of the series circuit can be obtained using the Pythagorean theorem: Z = sqrt(R^2 + Xc^2) = sqrt((1.1 x 10^3)^2 + (1061)^2) = 1529 Ohms. Finally, using Ohm's Law (v = iZ), the current (i) can be calculated by dividing the maximum voltage by the impedance: i = 170 / 1529 = 0.111 A.
Understanding AC Circuit Analysis
AC circuit analysis involves the calculation of various parameters in circuits that contain alternating current sources, resistors, and capacitors. In this specific scenario, we have an AC source operating at 60 Hz with a maximum voltage of 170 V connected in series with a resistor (R = 1.1 kΩ) and a capacitor (C = 2.5 μF).
The reactance of a capacitor in an AC circuit, denoted by Xc, is a crucial component in determining the impedance of the circuit. The formula Xc = 1/(2πfC) relates the reactance to the frequency and capacitance values. In this case, the calculated reactance of 1061 Ohms contributes to the total impedance of the series circuit, which is found to be 1529 Ohms using the Pythagorean theorem.
By applying Ohm's Law, the current flowing through the circuit can be determined by dividing the maximum voltage by the impedance. In this scenario, the current is calculated to be approximately 0.111 A. This analysis showcases the interconnected nature of components in an AC circuit and how their properties influence the overall behavior of the system.
By delving into AC circuit analysis, individuals can gain a deeper understanding of electrical circuits, enabling them to design, analyze, and troubleshoot various systems effectively. Mastering the calculations and principles involved in AC circuit analysis is essential for electrical engineers, technicians, and enthusiasts looking to enhance their skills in the field of electronics.