Skip to main content
Ch. 30 - Inductance, Electromagnetic Oscillations, and AC Circuits
Giancoli Douglas - Physics for Scientists and Engineers 5th edition
Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoGiancoli Douglas 5th editionCh. 30 - Inductance, Electromagnetic Oscillations, and AC CircuitsProblema 30.52
Capitolo 29, Problema 30.52

(II) A 25-mH coil whose resistance is 0.80 Ω is connected to a capacitor C and a 420-Hz source voltage. If the current and voltage are to be in phase, what value must C have?

Guida verificata passo dopo passo
1
Step 1: Understand that for the current and voltage to be in phase in an RLC circuit, the inductive reactance (XL) must equal the capacitive reactance (XC). The formula for inductive reactance is XL = 2\(\pi\) f L, where f is the frequency and L is the inductance.
Step 2: Calculate the inductive reactance using the given values: frequency (f = 420 Hz) and inductance (L = 25 mH = 0.025 H).
Step 3: Use the formula for capacitive reactance, which is XC = 1 / (2\(\pi\) f C), where C is the capacitance that needs to be calculated.
Step 4: Set the inductive reactance equal to the capacitive reactance (XL = XC) and solve for the capacitance C.
Step 5: Rearrange the equation to solve for C, which will be C = 1 / (2\(\pi\) f XL). Substitute the value of XL calculated in Step 2 to find the required capacitance.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
3m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Inductance and Resistance in RLC Circuits

In an RLC circuit, the inductance (L) and resistance (R) determine how the circuit responds to alternating current (AC). The inductance creates a magnetic field that opposes changes in current, while resistance dissipates energy. The relationship between these components affects the phase difference between voltage and current, which is crucial for understanding how to achieve in-phase conditions.
Video consigliato:
Percorso guidato
03:07
Unknown Resistance in an LR Circuit

Capacitance and Phase Relationship

Capacitance (C) is the ability of a capacitor to store charge. In an AC circuit, the capacitor causes the current to lead the voltage by 90 degrees. To achieve a condition where the current and voltage are in phase, the capacitive reactance must equal the inductive reactance, which can be calculated using the frequency of the source and the values of L and C.
Video consigliato:
Percorso guidato
08:02
Capacitors & Capacitance (Intro)

Resonance in RLC Circuits

Resonance occurs in RLC circuits when the inductive reactance equals the capacitive reactance, resulting in maximum current flow and voltage being in phase. This condition is characterized by a specific frequency known as the resonant frequency. The formula for resonance involves the inductance and capacitance values, allowing for the calculation of the required capacitance to achieve resonance at a given frequency.
Video consigliato:
Percorso guidato
05:23
Resonance in Series LRC Circuits
Pratica correlata
Domanda del libro di testo

Two tightly wound solenoids have the same length and circular cross-sectional area. But solenoid 1 uses wire that is 1.5 times as thick as solenoid 2. What is the ratio of their inductive time constants? (Assume the only resistance in the circuits is that of the wire itself.)

97
views
Domanda del libro di testo

Two tightly wound solenoids have the same length and circular cross-sectional area. But solenoid 1 uses wire that is 1.5 times as thick as solenoid 2.

(a) What is the ratio of their inductances?

(b) What is the ratio of their inductive time constants? (Assume the only resistance in the circuits is that of the wire itself.)

1362
views
Domanda del libro di testo

A 10.0-k Ω resistor is in series with a 34.0-mH inductor and an ac source. Calculate the impedance of the circuit if the source frequency is (a) 55.0 Hz; (b) 55.0 kHz.

1179
views
Domanda del libro di testo

(II) Suppose that the U-shaped conductor and connecting rod in Fig. 29–12a are oriented vertically (but still in contact) so that the rod is falling due to the gravitational force. Find the terminal speed of the rod if it has mass m = 3.6 grams, length 𝓁 = 18 cm, and resistance R = 0.0013 Ω. It is falling in a uniform horizontal field B = 0.080 T. Neglect the resistance of the U-shaped conductor, and friction.

1460
views
Domanda del libro di testo

A 1.50-k Ω resistor in series with a 370-mH inductor is driven by an ac power supply. At what frequency is the impedance double that of the impedance at 60.0 Hz?

1449
views
Domanda del libro di testo

(II) A capacitor is placed in parallel with some device, B, as in Fig. 30–18b, to filter out stray high-frequency signals, but to allow ordinary 60.0-Hz ac to pass through with little loss. Suppose that circuit B in Fig. 30–18b is a resistance R = 530 Ω connected to ground, and that C = 0.35 μF. Calculate the ratio of the capacitor’s current amplitude to the incoming current’s amplitude if the incoming current has a frequency of (a) 60.0 Hz; (b) 60.0 kHz.

1230
views