Question

A capacitor is connected across the terminals of an ac generator that has a frequency of $440 \mathrm{Hz}$ and supplies a voltage of $24 \mathrm{V} .$ When a second capacitor is connected in parallel with the first one, the current from the generator increases by 0.18 A. Find the capacitance of the second capacitor.

Name: Problem 5, Chapter 23: Physics
Uploaded: 2020-05-18T20:32:17-08:00
Duration: 4 min 53 s
Channel: Breanna Kloczkowski
Description: A capacitor is connected across the terminals of an ac generator that has a frequency of 440 Hz and supplies a voltage of 24 V . When a second capacitor is connected in parallel with the first one, the current from the generator increases by 0.18 A. Find the capacitance of the second capacitor.

   A capacitor is connected across the terminals of an ac generator that has a frequency of $440 \mathrm{Hz}$ and supplies a voltage of $24 \mathrm{V} .$ When a second capacitor is connected in parallel with the first one, the current from the generator increases by 0.18 A. Find the capacitance of the second capacitor.

Physics

John D. Cutnell,… 11th Edition

Chapter 23, Problem 5

Instant Answer

Solved by Expert Breanna Kloczkowski

05/18/2020

Step 1

First, we need to find the reactance of the first capacitor. The formula for capacitive reactance (Xc) is: Xc = 1 / (2 * π * f * C) where f is the frequency and C is the capacitance. Show more…

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A capacitor is connected across the terminals of an ac generator that has a frequency of $440 \mathrm{Hz}$ and supplies a voltage of $24 \mathrm{V} .$ When a second capacitor is connected in parallel with the first one, the current from the generator increases by 0.18 A. Find the capacitance of the second capacitor.

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Key Concepts

AC Circuit Fundamentals

This concept involves understanding how alternating current (AC) circuits behave, notably with sinusoidal voltage and current waveforms. It includes ideas like RMS (root mean square) values, phasor representations, and how these concepts are used to analyze how various circuit components respond to AC signals.

Capacitive Reactance

Capacitive reactance is the opposition offered by a capacitor to the change in voltage in an AC circuit. It is defined by the relation Xc = 1/(2?fC), where f is the frequency and C is the capacitance. This concept is crucial for analyzing how capacitors affect the current and phase in AC systems.

Parallel Combination of Capacitors

When capacitors are connected in parallel, their individual capacitances add directly to yield the total capacitance. This simple addition impacts the overall capacitive reactance and, consequently, the amount of current a capacitor draws when subjected to an AC voltage source.

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