Ch 31: Alternating Current

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

Young & Freedman Calc 14th Edition

Ch 31: Alternating Current

Problem 4a

Chapter 31, Problem 4a

A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. 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

Understand the relationship between voltage and current in an AC circuit with a capacitor. In such a circuit, the current leads the voltage by a phase angle due to the capacitive reactance.

Recall the formula for the phase angle \( \Phi \) in a capacitive circuit, which is given by \( \Phi = -\frac{\pi}{2} \). This indicates that the voltage lags the current by 90 degrees.

Recognize that the negative sign in the phase angle formula indicates that the voltage lags behind the current.

Since the phase angle \( \Phi \) is \( -\frac{\pi}{2} \), the source voltage lags the current by 90 degrees.

Conclude that in a purely capacitive AC circuit, the phase angle is always \( -\frac{\pi}{2} \), meaning the voltage lags the current by 90 degrees.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Capacitive Reactance

Capacitive reactance (Xc) is the opposition a capacitor offers to the flow of alternating current (AC). It is inversely proportional to the frequency (f) of the AC source and the capacitance (C) of the capacitor, given by the formula Xc = 1/(2πfC). This concept is crucial for understanding how the capacitor affects the phase relationship between voltage and current.

Phase Angle in AC Circuits

The phase angle (Φ) in AC circuits indicates the difference in phase between the voltage across and the current through a component. For a purely capacitive circuit, the current leads the voltage by 90 degrees, meaning the phase angle is -90 degrees. This concept helps determine whether the voltage leads or lags the current in the circuit.

Voltage and Current Relationship in Capacitors

In capacitors connected to an AC source, the current leads the voltage because the capacitor charges and discharges, causing the current to reach its peak before the voltage does. This relationship is essential for understanding the behavior of capacitors in AC circuits and determining the phase angle between voltage and current.

Recommended video:

Guided course

07:14

RMS Current and Voltage

Related Practice

Textbook Question

(a) Compute the reactance of a 0.450-H inductor at frequencies of 60.0 Hz and 600 Hz. (b) Compute the reactance of a 2.50-μF capacitor at the same frequencies. (c) At what frequency is the reactance of a 0.450-H inductor equal to that of a 2.50-μF capacitor?

views

Textbook Question

You have a special light bulb with a very delicate wire filament. The wire will break if the current in it ever exceeds 1.50 A, even for an instant. What is the largest root-mean-square current you can run through this bulb?

views

Textbook Question

A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. What is the capacitance C of the capacitor if the current amplitude is 5.30 A?

views

Textbook Question

A capacitance C and an inductance L are operated at the same angular frequency. (a) At what angular frequency will they have the same reactance? (b) If L = 5 00 mH and C = 3.50 μF, what is the numerical value of the angular frequency in part (a), and what is the reactance of each element?

views

Textbook Question

The voltage across the terminals of an ac power supply varies with time according to Eq. (31.1) v = Vcosωt. The voltage amplitude is V = 45.0 V. What are (a) the root-mean-square potential difference V_rms and (b) the average potential difference V_av between the two terminals of the power supply?

views

Textbook Question

A sinusoidal current i = I cosωt has an rms value I_rms = 2.10 A. What is the current amplitude?

views