Final answer:
To determine the voltage and current of each component in an AC circuit, we consider phase relationships and reactance. Voltages in inductors lead and in capacitors lag the current by 90 degrees. The formula for the capacitive reactance (XC) is XC = 1/(ωC), and VC = I ⋅ XC can be used to determine the voltage across the capacitor.
Step-by-step explanation:
To find the voltage and current of each capacitor and inductor in the circuit described, we start by understanding the phase relationships between the voltage and current in these components.
Conservation of charge means that the current remains the same throughout the circuit.
For the inductors and capacitors in AC circuits, the voltage and current are out of phase with each other.
For inductors, the voltage (VL) leads the current by 90 degrees (one-fourth of a cycle), while for capacitors, the voltage (VC) lags the current by 90 degrees.
This phase difference is due to the inductive and capacitive reactance of the components which opposes changes in current and voltage, respectively.
To calculate the voltages across the inductor (VL) and the capacitor (VC), we need to know the angular frequency of the source (omega = 2πf) where f is the frequency, and the values of the inductance (L) and capacitance (C).
By using Kirchhoff's loop rule, the sum of the instantaneous voltages in the loop equals the source voltage (V = VR + VL + VC).
The voltage across the resistor (VR) is in phase with the current. Readings from an AC voltmeter across an inductor would give us VL, which can be calculated using VL = I ⋅ XL, where XL is the inductive reactance given by XL = ωL.
Capacitive reactance (XC) is given by XC = 1/( ωC), and the voltage across the capacitor (VC) can be calculated using VC = I ⋅ XC.
Question: Find the voltage and current of each capacitor and inductor in the circuit below.
A complex electrical circuit composed of capacitors and inductors arranged in a strategic configuration. The circuit consists of a power source, capacitors C 1and C 2 , and inductors L 1 and L2. The circuit is in a steady state, and the values of the components are known.