Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 28: Problem 67

Two capacitors are connected in parallel across a \(10-\mathrm{V}\) rms, \(10-\mathrm{kHz}\) sine-wave generator, and the generator supplies a total rms current of 30 mA. With capacitors rewired in series, the rms generator current drops to 5.5 mA. Find the two capacitances.

Short Answer

Expert verified
The values for the two capacitances \(C_1\) and \(C_2\) can be calculated by solving the two simultaneous equations derived from the analysis of the series and parallel connections.

Step by step solution

01

Apply fundamental principle for capacitors connected in parallel.

In this scenario, the total current is the sum of currents flowing through each capacitor. Let the values of the two capacitors be \(C_1\) and \(C_2\). We can calculate the equivalent impedance for the capacitors in parallel using the formula from the relationship: \(I = V/Z\), where \(I\) is the current, \(V\) is the voltage, and \(Z\) is the impedance. The impedance of a capacitor is given by formula \(Z = 1/( 2\pi fC) \), here \(f\) is the frequency. So for two capacitors in parallel, the total impedance \(Z_t\) can be calculated as \( Z_t = 1/( (I/V)_{total} = 1/(2\pi f(C_1 + C_2)) \)
02

Consider the capacitors connected in series.

In this case, the equivalent capacitance can be calculated with the formula: \(1/C_t = 1/C_1 + 1/C_2\). But current drops, so we need to calculate the total impedance again with the new current and same voltage: \(Z_s = V/(I_s) = 1/(2\pi f\cdot C_t) \). And equivalent capacitance can be calculated as \(C_t = 1/( 2\pi f\cdot Z_s) \)
03

Solve for the values of the capacitors.

We now have two equations: one for parallel connection and another one for series connection. The total capacitance in both cases is equal \(C_1 + C_2 = C_t\). We can then use these to find the capacitances. Using simultaneous equations, we can find the value for \(C_1\) and \(C_2\) .

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Your professor tells you about the days before digital computers when engineers used electric circuits to model mechanical systems. Suppose a \(5.0-\mathrm{kg}\) mass is connected to a spring with \(k=1.44 \mathrm{kN} / \mathrm{m} .\) This is then modeled by an \(L C\) circuit with \(L=2.5 \mathrm{H} .\) What should \(C\) be in order for the \(L C\) circuit to have the same resonant frequency as the mass-spring system?

(a) A \(2.2-\) H inductor is connected across \(120-\mathrm{V}\) rms, \(60-\mathrm{Hz}\) power. Find the rms inductor current. (b) Repeat if the same inductor is connected across the \(230-\mathrm{V}\) rms, \(50-\mathrm{Hz}\) power commonly used in Europe.

For \(R L C\) circuits in which the resistance isn't too high, the \(Q\) factor may be defined as the ratio of the resonant frequency to the difference between the two frequencies where the power dissipated in the circuit is half the power dissipated at resonance. Using suitable approximations, show that this definition leads to \(Q=\omega_{0} L / R,\) with \(\omega_{0}\) the resonant frequency.

What's meant by the statement, "A capacitor acts like a DC open circuit"?

Connections to the body for electrocardiography (ECG) and electroencephalography (EEG) are normally made with metal electrodes and conductive gels to ensure good electrical contact. An alternative is the capacitively coupled noncontact electrode, which uses a conductor near but not contacting the skin, to form a capacitor. Clothing can serve as the capacitor's insulation, eliminating skin contact. A particular EEG instrument calls for capacitive electrodes with maximum reactance \(10 \mathrm{M} \Omega\) at a typical EEG beta wave frequency of 25 Hz. What's the minimum electrode capacitance?
See all solutions

Recommended explanations on Physics Textbooks

Engineering Physics

Read Explanation

Measurements

Read Explanation

Thermodynamics

Read Explanation

Medical Physics

Read Explanation

Linear Momentum

Read Explanation

Radiation

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free