A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. (a) What is the phase angle Φ for the source voltage relative to the current? Does the source voltage lag or lead the current?

Verified step by step guidance

1. Identify the type of circuit component involved. In this case, it's a capacitor connected to an AC source.
2. Recall that in a purely capacitive circuit, the current leads the voltage by 90 degrees. This is due to the property of capacitors where they allow current to flow when they are charging up, which happens before the voltage across them reaches its peak.
3. Write the expression for the phase angle Φ in a capacitive circuit. For a purely capacitive circuit, Φ = -90°.
4. Determine the relationship between the source voltage and the current based on the phase angle. A negative phase angle indicates that the voltage lags the current.
5. Conclude that the source voltage lags the current by 90 degrees in this capacitive circuit.

Key Concepts

Capacitive Reactance

Capacitive reactance (Xc) is the opposition that a capacitor offers to alternating current (AC) due to its capacitance. It is calculated using the formula Xc = 1/(2πfC), where f is the frequency and C is the capacitance. This reactance causes a phase shift between the voltage across the capacitor and the current flowing through it, which is crucial for understanding the behavior of capacitors in AC circuits.

Phase Angle

The phase angle (Φ) in an AC circuit indicates the difference in phase between the voltage and the current waveforms. For a capacitor, the current leads the voltage by 90 degrees (or π/2 radians). This phase relationship is essential for analyzing how capacitors affect the overall impedance and power factor in AC circuits.

Impedance in AC Circuits

Impedance (Z) is the total opposition that a circuit presents to the flow of alternating current, combining both resistance (R) and reactance (X). In a purely capacitive circuit, the impedance is purely reactive and can be expressed as Z = jXc, where j is the imaginary unit. Understanding impedance is vital for determining how voltage and current interact in AC circuits, particularly in relation to phase angles.