For an ac circuit with resistance 145 m Ω, capacitance 10.0 μF, frequency 72.5 kHz, and E=7.00

step 1 Hi, in the given problem there is a circuit which is having a resistance r is equal to 145 milli

For an ac circuit with resistance 145 m Ω, capacitance 10.0...

For an ac circuit with resistance $145 \mathrm{~m} \Omega$, capacitance $10.0 \mu \mathrm{F}$, frequency $72.5 \mathrm{kHz},$ and $E=7.00 \mathrm{mV}:$ (a) find the impedance (in ohms), (b) find the phase angle, and (c) find the current.

Key Concepts

Ohm’s Law for AC Circuits

Ohm’s Law in the context of AC circuits extends the concept of the relationship between voltage, current, and resistance by incorporating impedance instead of resistance alone. The law is expressed as I = V/Z, where I is the current, V is the applied voltage, and Z is the magnitude of the impedance. This formulation is crucial for calculating current in AC circuits where reactive components cause phase differences between voltage and current.

Phase Angle

The phase angle in an AC circuit quantifies the phase difference between the voltage and the current, arising due to the presence of reactive components like capacitors. In an RC circuit, this angle is calculated using the arctan of the ratio of capacitive reactance to resistance (? = -arctan(X_C/R)), indicating that the current leading or lagging the voltage. The phase angle is essential for understanding the timing of the peaks of voltage and current relative to each other.

Capacitive Reactance

Capacitive reactance represents the opposition a capacitor offers to the change of voltage in an AC circuit. It varies inversely with both the frequency of the applied voltage and the capacitance of the capacitor, given by the formula X_C = 1/(?C), where ? (omega) is the angular frequency equal to 2? times the frequency. This concept is crucial in determining how a capacitor influences the circuit’s behavior at different frequencies.

Impedance

Impedance in an AC circuit is the complete measure of opposition to current flow, incorporating both resistance (the opposition to current due to energy dissipation) and reactance (the opposition due to stored energy in capacitors or inductors). For AC circuits with capacitors, the total impedance is computed as the vector sum of the resistive and capacitive components, typically using the relation Z = sqrt(R² + X_C²), where X_C is the capacitive reactance.

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