A capacitor and a resistor are connected in parallel to a 120-V, 60-Hz line. The resistor has a

step 1 Hi, in the given problem, this is a series RC circuit in which RMS voltage is given to be 110 vo

A capacitor and a resistor are connected in parallel to a...

A capacitor and a resistor are connected in parallel to a $120-\mathrm{V}, 60-\mathrm{Hz}$ line. The resistor has a resistance of $40 \Omega$, and the capacitor has a capacitance of $132.6 \mu \mathrm{F}$. What is the total current flow through the circuit?

Key Concepts

Phasor Addition in AC Circuits

In AC circuits, currents and voltages are represented as phasors, which are vectors in the complex plane that encapsulate both magnitude and phase. When circuit elements like resistors and capacitors are connected in parallel, their individual currents—each with its respective phase angle—must be combined using vector (phasor) addition to accurately determine the total current flowing through the circuit.

AC Circuit Analysis

This concept involves analyzing circuits that operate with alternating current, where voltages and currents vary sinusoidally with time. In these analyses, the circuit elements (such as resistors, capacitors, and inductors) behave based on their frequency-dependent impedances, requiring the use of phasor representations to capture both magnitude and phase relationships.

Resistor Behavior in AC Circuits

In AC circuits, a resistor’s behavior is straightforward since its impedance is purely real, meaning that the voltage across and current through the resistor remain in phase. The current through a resistor can be directly calculated using Ohm's law (I = V/R), which is similar to DC circuits but applied to the instantaneous or RMS values of voltage and current.

Capacitive Reactance

Capacitive reactance is the opposition that a capacitor offers to the flow of alternating current, and it varies inversely with both the frequency of the AC source and the capacitance value. It is defined by the formula Xc = 1/(2?fC), and unlike resistance, it introduces a 90-degree phase lead of the current with respect to the voltage.

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