## DC Circuits - Problem Solving

Example problem on ohm's law: the basic circuit.

An emf source of \(6.0V\) is connected to a purely resistive lamp and a current of \(2.0\) amperes flows. All the wires are resistance-free. What is the resistance of the lamp?

- Where in the circuit does the gain in potential energy occur?
- Where in the circuit does the loss of potential energy occur?
- What is Ohm's Law?

The gain of potential energy occurs as a charge passes through the battery, that is, it gains a potential of \(\varepsilon = 6.0V\) . No energy is lost to the wires, since they are assumed to be resistance-free. By conservation of energy, the potential that was gained (i.e. \(\varepsilon= V = 6.0V\) ) must be lost in the resistor. So, by Ohm's Law:

\(V = I R\)

\(R = 3.0 \Omega\)

## Example of Problem on Resistors in Series

- How are resistors related when connected in series?
- What is true about potential drops of resistors when connected in series?
- You will need to use Ohm's Law.

First, let's label the diagram with the information given in the question.

\(R_1 = \frac {V_1}{I}, R_2 = \frac{V_2}{I} , R_3 = \frac {V_3}{I}\)

\(R_ \mathrm {equivalent} = R_1 + R_2 +R_3+R_4\)

\(R_4 = R _\mathrm {equivalent} - ( R_1+R_2+R_3)\)

\(R_4 = 30 - (5.0 + 8.0 + 7.0) = 10 \Omega\)

\(V_4 = (1.0)\cdot (10) = 10V\)

## Example Problem on Resistors in Parallel

In the following schematic diagram, find the total current, I.

- You will need Ohm's Law.
- How are resistors related when connected in parallel?
- What is the potential drop across each resistor?
- How does current behave in parallel branches?

We know the total potential of this circuit,

\(V_1 = V_2 = V_3 = \varepsilon = 12.0V\)

to find the current across each resistor.

\(I_1 = \frac {V_1}{R_1} = \frac {12.0V}{2.0 \Omega} = 6.0A\)

\(I_2 = \frac{V_2}{R_2} = \frac{12.0V}{3.0 \Omega} = 4.0A\)

\(I_3 = \frac {V_3}{R_3} = \frac {12.0V}{6.0 \Omega} = 2.0A\)

So, adding up the three currents, we get:

So, the total current is \( I = 12.0A\) .

## Example Problems on Resistors in Combination Circuits

- Which resistors are in parallel and which are in series?
- Is this circuit composed of small groups of parallel resistors, all connected in series? Or is it composed of groups of series resistors, connected in parallel?

First, we will find the equivalent resistance between \(A\) and \(B\) .

\(\frac {1}{R_\mathrm{equivalent}} = \sum \frac{1}{R_i}\)

\(\frac {1}{R_{AB}} = \frac {1}{R_1} + \frac {1}{R_2}\)

\(= \frac {1}{10.0}+ \frac{1}{4.0}\)

\(\frac {1}{R_{CD}} = \frac {1}{R_4} + \frac {1}{R_5}\)

\(\frac {1}{R_{CD}} = \frac{1}{8.0}+\frac{1}{1.0}\)

we can find the equivalent resistance of the circuit.

So the equivalent resistance of this circuit is \(R = 6.7 \Omega\) .

\(R_\mathrm {equivalent} = \sum R_i\)

Now, in branch \(CD\) there is only one resistor, so this branch cannot be simplified further.

\(\frac {1}{R_\mathrm {equivalent}} = \sum \frac {1}{R_i}\)

we can find the equivalent resistance of these branches.

\(\frac {1}{R} = \frac {1}{R_{AB}} + \frac {1}{R_3}+ \frac{1}{R_{EF}}\)

\(\frac{1}{R} = \frac{1}{3.0} + \frac{1}{3.0}+ \frac{1}{9.0}\)

## AP Physics 2: Circuits Practice Problems with Answers

## Circuit Practice Problems

Problem (1): In the circuit below, find the equivalent resistance between points $A$ and $B$.

Problem (4): In the circuit below, how much current passes through the $1.5-{\rm \Omega}$ resistor?

Further reading: Ohm's law Practice problems with solutions

Further Reading: Kirchhoff's law solved problems for the AP Physics C exam

With this long introduction, let's move on to solving the problem.

Conversely, after passing a long time, it behaves like a resistor with infinite resistance.

Author : Dr. Ali Nemati Page Published : 10/13/2021

© 2015 All rights reserved. by Physexams.com

## Physics Problems with Solutions

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## Unit: Circuit analysis

- Ideal circuit elements (Opens a modal)
- Ideal sources (Opens a modal)
- Ideal elements and sources (Opens a modal)
- Real-world circuit elements (Opens a modal)
- Circuit terminology (Opens a modal)
- Sign convention for passive components (Opens a modal)
- Sign convention for passive components and sources (Opens a modal)

## Resistor circuits

- Series resistors (Opens a modal)
- Parallel resistors (part 1) (Opens a modal)
- Parallel resistors (part 2) (Opens a modal)
- Parallel resistors (part 3) (Opens a modal)
- Parallel resistors (Opens a modal)
- Parallel conductance (Opens a modal)
- Simplifying resistor networks (Opens a modal)
- Delta-Wye resistor networks (Opens a modal)
- Voltage divider (Opens a modal)
- Analyzing a resistor circuit with two batteries (Opens a modal)
- Series and parallel resistors 8 questions Practice

## DC circuit analysis

- Circuit analysis overview (Opens a modal)
- Kirchhoff's current law (Opens a modal)
- Kirchhoff's voltage law (Opens a modal)
- Kirchhoff's laws (Opens a modal)
- Labeling voltages (Opens a modal)
- Application of the fundamental laws (setup) (Opens a modal)
- Application of the fundamental laws (solve) (Opens a modal)
- Application of the fundamental laws (Opens a modal)
- Node voltage method (steps 1 to 4) (Opens a modal)
- Node voltage method (step 5) (Opens a modal)
- Node voltage method (Opens a modal)
- Mesh current method (steps 1 to 3) (Opens a modal)
- Mesh current method (step 4) (Opens a modal)
- Mesh current method (Opens a modal)
- Loop current method (Opens a modal)
- Number of required equations (Opens a modal)
- Linearity (Opens a modal)
- Superposition (Opens a modal)

## Natural and forced response

- Capacitor i-v equations (Opens a modal)
- A capacitor integrates current (Opens a modal)
- Capacitor i-v equation in action (Opens a modal)
- Inductor equations (Opens a modal)
- Inductor kickback (1 of 2) (Opens a modal)
- Inductor kickback (2 of 2) (Opens a modal)
- Inductor i-v equation in action (Opens a modal)
- RC natural response - intuition (Opens a modal)
- RC natural response - derivation (Opens a modal)
- RC natural response - example (Opens a modal)
- RC natural response (Opens a modal)
- RC step response - intuition (Opens a modal)
- RC step response setup (1 of 3) (Opens a modal)
- RC step response solve (2 of 3) (Opens a modal)
- RC step response example (3 of 3) (Opens a modal)
- RC step response (Opens a modal)
- RL natural response (Opens a modal)
- Sketching exponentials (Opens a modal)
- Sketching exponentials - examples (Opens a modal)
- LC natural response intuition 1 (Opens a modal)
- LC natural response intuition 2 (Opens a modal)
- LC natural response derivation 1 (Opens a modal)
- LC natural response derivation 2 (Opens a modal)
- LC natural response derivation 3 (Opens a modal)
- LC natural response derivation 4 (Opens a modal)
- LC natural response example (Opens a modal)
- LC natural response (Opens a modal)
- LC natural response - derivation (Opens a modal)
- RLC natural response - intuition (Opens a modal)
- RLC natural response - derivation (Opens a modal)
- RLC natural response - variations (Opens a modal)

## AC circuit analysis

- AC analysis intro 1 (Opens a modal)
- AC analysis intro 2 (Opens a modal)
- Trigonometry review (Opens a modal)
- Sine and cosine come from circles (Opens a modal)
- Sine of time (Opens a modal)
- Sine and cosine from rotating vector (Opens a modal)
- Lead Lag (Opens a modal)
- Complex numbers (Opens a modal)
- Multiplying by j is rotation (Opens a modal)
- Complex rotation (Opens a modal)
- Euler's formula (Opens a modal)
- Complex exponential magnitude (Opens a modal)
- Complex exponentials spin (Opens a modal)
- Euler's sine wave (Opens a modal)
- Euler's cosine wave (Opens a modal)
- Negative frequency (Opens a modal)
- AC analysis superposition (Opens a modal)
- Impedance (Opens a modal)
- Impedance vs frequency (Opens a modal)
- ELI the ICE man (Opens a modal)
- Impedance of simple networks (Opens a modal)
- KVL in the frequency domain (Opens a modal)

## About this unit

## Diode Circuit Analysis

## Load Line Analysis

## Mathematical Model

## Ideal Diode Model

The third step is now doing some basic circuit analysis to see if our assumptions actually work.

## Constant Voltage Drop Model

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## How to Solve Parallel Circuits

Last Updated: October 27, 2022 References Approved

## Cheat Sheet

- Total resistance R T for resistors in parallel: 1 / R T = 1 / R 1 + 1 / R 2 + 1 / R 3 + ...
- Voltage is always the same across branches: V T = V 1 = V 2 = V 3 = ...
- Total current I T = I 1 + I 2 + I 3 + ...
- Ohm's Law: V = IR

## Introduction to Parallel Circuits

- For example, a circuit has two resistors in parallel, each with 4Ω resistance. 1 / R T = 1 /4Ω + 1 /4Ω → 1 / R T = 1 /2Ω → R T = 2Ω. In other words, two branches of equal resistance are exactly twice as easy to get through as one branch alone.
- If one branch has no resistance (0Ω), all the current goes through that branch. The total resistance is 0. [6] X Research source

## Example Circuit

## Additional Calculations

- Two resistors in parallel: I 1 = I T R 2 / (R 1 + R 2 )
- More than two resistors in parallel: To solve for I 1 , find the combined resistance of all resistors besides R 1 . Remember to use the formula for resistors in parallel. Now use the equation about, replacing R 2 with your answer.

## Community Q&A

## Video . By using this service, some information may be shared with YouTube.

- If solving Series-Parallel circuits, solve the Parallel parts first. Then you are left with a much easier Series circuit. ⧼thumbs_response⧽ Helpful 24 Not Helpful 5
- You may have been taught Ohm's Law as E = IR or V = AR. These are just different notations, meaning the same thing. ⧼thumbs_response⧽ Helpful 12 Not Helpful 5
- In a Parallel circuit the same voltage is applied across all the resistors. ⧼thumbs_response⧽ Helpful 47 Not Helpful 39

## You Might Also Like

- ↑ https://www.swtc.edu/ag_power/electrical/lecture/parallel_circuits.htm
- ↑ https://www.physicsclassroom.com/class/circuits/Lesson-4/Parallel-Circuits
- ↑ https://pressbooks.bccampus.ca/basicelectricity/chapter/ground/
- ↑ http://www.tpub.com/neets/book1/chapter3/1-34.htm
- ↑ https://workforce.libretexts.org/Bookshelves/Electronics_Technology/Book%3A_Electric_Circuits_I_-_Direct_Current_(Kuphaldt)/05%3A_Series_And_Parallel_Circuits/5.03%3A_Simple_Parallel_Circuits
- ↑ https://www.allaboutcircuits.com/textbook/direct-current/chpt-5/simple-parallel-circuits/
- ↑ https://www.allaboutcircuits.com/textbook/direct-current/chpt-5/power-calculations/
- ↑ http://physics.bu.edu/py106/notes/Circuits.html
- ↑ https://www.wilsonware.com/electronics/kirchhoff.htm

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## DC Circuits

Chad Davis, University of Oklahoma

Publisher: University of Oklahoma Libraries

## Formats Available

Reviewed by Amr Metwally, Instructor, Oregon Institute of Technology on 4/19/20

Comprehensiveness rating: 3 see less

The text book provides accurate information to the best of my knowledge.

Organization/Structure/Flow rating: 5

The links I used worked well. The hand written Appendix A1 does not look professional.

I could not notice any grammatical errors.

I could not see any cultural issues.

In general, the book is a valuable free reference book.

Comprehensiveness rating: 4 see less

I found the contents in the book accurate to the best of my knowledge.

I think the book is organized well.

The text contains no grammatical errors.

The contents are purely technical. So it has no cultural relevance.

Reviewed by Jacob LeBlanc, Instructor, University of Louisiana at Lafayette on 11/10/19

Provides extensive information relating to DC circuits, but electromagnetism material is limited.

RC charging capacitor circuit could be more simplified.

Organization/Structure/Flow rating: 4

Did not notice any problems. Author caters to beginners, intermediates, and experts alike.

Comprehensiveness rating: 5 see less

It will last a lifetime. Already has with few exceptions.

Stepped through all points of contention very well, though some points more quickly than others.

This follows the material exactly as I teach it.

I didn't find any grammatical errors.

There is no "person" involved in presenting this material to anyone. So, no cultural biases.

Reviewed by Mahbube Siddiki, Instructor, University of Missouri-Kansas City on 8/2/18

Topics covered in the book seems to be unbiased and error free.

The book is well written in a modular fashion. Topics are divided into modules and submodules.

The book is well organized, contents are presented in a logical and sequential order.

No grammatical error was noticed.

No culturally insensitive or offensive material was found throughout the text.

Reviewed by Sangho Bok, Assistant Professor, Southern Utah University on 6/19/18

The material for DC circuit analysis looks accurate and unbiased.

The modules of the book look well-organized and the sub-modules are divided properly.

No grammatical error has been noticed.

There is no culturally insensitive or offensive content.

Reviewed by Edwin Hou, Professor, New Jersey Institute of Technology on 5/21/18

The content of the book appears to be error-free and unbiased.

The textbook is clearly written. Examples are worked out in details.

The terminology used throughout the textbook is consistent.

Within each module, the topics are further divided into sections and is well organized.

The topics in circuit analysis are presented in a logical and clear fashion.

For the sections I examined in detail, there were no grammatical errors.

I did not see any culturally insensitive or offensive material in the textbook.

This book is useful as a textbook or as a reference in DC circuit analysis.

Reviewed by Huimin Chen, associate professor, University of New Orleans on 3/27/18

The book has good modular sections covering the key skill set for DC circuit analysis.

I do not see any grammatical error.

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## Table of Contents

PrefaceModule 1 – The Basics of DC Circuits with Resistors

- Section 1.1 – Introduction and Basic Definitions
- Section 1.1.1 - Charge vs Current
- Section 1.1.2 - Resistance Calculations – (Resistance explained in more detail in section 1.1.3)
- Section 1.1.3 - Ohm's Law: Voltage, Current, Resistance, and Conductance
- Section 1.1.4 – Power and Energy
- Section 1.2 – Combining Resistors in Parallel or Series
- Section 1.3 – Kirchhoff's Voltage Law (KVL) and Voltage Divider Rule (VDR)
- Section 1.4 – Kirchhoff's Current Law (KCL) and Current Divider Rule (CDR)
- Module 1 – Equation List

Module 2 – Advanced Topics for DC Circuits with Resistors

- Section 2.1 – Source Transformations: Thevenin and Norton Form
- Section 2.2 – Approximate Source Transformations: Adding a virtual resistor
- Section 2.2.1 - Voltage Source Approximate Transformation
- Section 2.2.2 - Current Source Approximate Transformation
- Section 2.3 – Mesh Matrix Analysis and traditional loop analysis methods
- Section 2.4 – Nodal Matrix Analysis and traditional Nodal Analysis
- Section 2.5 – Superposition: Solving a circuit by including only one source at a time
- Section 2.6 – Thevenin and Norton Equivalent Circuits

Module 3 – DC Circuits with Resistors, Capacitors, and Inductors

- Section 3.1 – Background for Capacitors
- Section 3.2 – Background for Inductors
- Section 3.3 – Combining Inductors in Parallel and/or Series
- Section 3.4 – Combining Capacitors in Parallel and/or Series
- Section 3.5 – DC Transient Analysis with RC and RL Circuits
- Section 3.5.1 – Single Loop RL and RC Charging (Store) Circuits
- Section 3.5.2 – Single Loop RL and RC Discharging (Release) Circuits
- Section 3.6 – DC Steady State Analysis with RC, RL, and RLC Circuits
- Section 3.7 – Introduction to Passive Filters
- Module 3 – Equation List

References and LinksAppendix – Dependent Sources and Laplace Transform Examples

## Ancillary Material

## About the Book

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## Dc circuit math problems

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## DC Circuits

## Solve DC Circuits Problems

Parallel dc circuits practice worksheet with answers.

Solving typical dc/dc converter application problems

CONVERSI.MAR–Conversion Devices, Inc.–SC–12– –##

Here are some simple guidelines to help ensure maximum performance and reliability

BY ANASTASIOS SIMOPOULOS and STEVE FORRESTER Conversion Devices, Inc. Brockton, MA

Opening shot: Dc/dc converters form an integral part of many power distribution systems.

Fig. 1. Most dc/dc converters have an input filter stage with capacitors that charge at a slow rate.

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## IMAGES

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DC Circuits - Problem Solving Example Problem on Ohm's Law: The Basic Circuit Question An emf source of 6.0 V is connected to a purely resistive lamp and a current of 2.0 amperes flows. All the wires are resistance-free. What is the resistance of the lamp? Figure 1: Diagram of the circuit in this problem. Hints

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

There are many ways to solve the above system. One way is to use equation (XIII) and substitute i_1 by i_2 + i_3 in equations (XI) and (XII) to obtain a system with two unknowns 100 (i_2 + i_3) + 300 i_2 = 20 (14) 300 i_2 - 50 i_3 = - 5 (15) Rearrange to rewrite the above system as 400 i_2 + 100 i_3 = 20 (16) 300 i_2 - 50 i_3 = - 5 (17)

The problem is, how do you operate an LED from a typical electronic power source, which may output 24 volts DC or more? The answer is to use a series dropping resistor: Calculate the necessary resistance value and minimum power rating of a series dropping resistor for an LED rated at 1.7 volts and 20 mA, and a power supply voltage of 24 volts.

Parallel DC Circuits Practice Worksheet With Answers Basic Electricity PDF Version Question 1 In this circuit, three resistors receive the same amount of voltage (24 volts) from a single source. Calculate the amount of current "drawn" by each resistor, as well as the amount of power dissipated by each resistor: Question 2

Step 1: Let's take stock of the circuit. It obviously only has one loop, and we've got a voltage source and two resistors. We've been given the value of the voltage source and both resistors, so all we need is to find out the current around the loop and the voltage drops over the resistors. And as soon as we find one, we can quickly use ...

DC circuit #1 See solution ↓ Circuit #2 Determine I and UAB. If U s1 and U s2 represent two ideal batteries, which one charges the other? U s1 = 120V U s2 = 90V R 1 = R 2 = 10Ω R 3 = 40Ω DC circuit #2 See solution ↓ Circuit #3 Calculate the resistance RG seen by the generator, and I1. Then, using the voltage division rule, calculate I2 and I3.

Solution : One of the typical questions in all circuit practice problems is finding the equivalent resistance of a given circuit. Recall that the equivalent of two resistors in series is R_ {eq}=R_1+R_2 Req = R1 + R2 and in parallel is \frac {1} {R_ {eq}}=\frac {1} {R_1}+\frac {1} {R_2} Req1 = R11 + R21 .

Voltages and Currents Calculator for Circuit 3. Enter the voltage source Vin in volts and the resistors R1, R2, R3, R4 and R5 in Ω and press "Calculate". The calculator uses the above formulas to calculates all currents and voltages whose formulas were obtained above. R1 =. 10.

Resistive Circuit Solver Simulate Simulate any kind of circuit you have designed and get the results instantly on just a single click. Design Design your own custom circuit using the components given in the palette in the web editor by simple drag and drop

5. Find the equivalent resistance of the circuit shown below. Find the voltage drop over, current through, and power dissipated by each resistor. Put your results in a table. We reduce circuits which are a combination of series and parallel resistors piece by piece. Examining the

Solving DC Circuit Problems Some Guidelines. Suggested Strategy Apply Kirchhoff's Rules To The Chart Method (see the 152 Web Page) Kirchhoff's Rules There are ways in which resistors can be connected so that the circuits formed cannot be reduced to a single equivalent resistor.

Circuit analysis is the process of finding all the currents and voltages in a network of connected components. We look at the basic elements used to build circuits, and find out what happens when elements are connected together into a circuit. ... DC circuit analysis. Learn. Circuit analysis overview (Opens a modal) Kirchhoff's current law ...

In this tutorial, we are going to discuss the Q-point of a diode and use few diode circuit problems to show how to solve diode circuits. We will discuss four methods of solving diode circuits: load line analysis, mathematical model, ideal diode circuit analysis, and constant voltage drop diode…

Solve for total resistance. You can find this in two different ways. You can use the resistance row to calculate it using the formula 1 / RT = 1 / R1 + 1 / R2 + 1 / R3. However, it's often easier to solve for it using Ohm's Law and the total V and I values. When solving for resistance, rearrange Ohm's Law as R = V/I Part 3 Additional Calculations 1

How do you analyze a circuit with resistors in series and parallel configurations? With the Break It Down-Build It Up Method! http://www.jesseleemason.com Mu...

This physics video tutorial explains how to solve any resistors in series and parallel combination circuit problems. The first thing you need to do is calculate the equivalent resistance of...

Module 2 covers more difficult problem solving techniques for circuits that include only DC sources and resistors. Module 3 introduces capacitors and inductors. These non-linear reactive components are analyzed in the transient and steady state regions in circuits with DC sources in Module 3.

The basic tools for solving DC circuit problems are Ohm's Law, the power relationship, the voltage law, and the current law. The following configurations are typical; details may be examined by clicking on the diagram for the desired circuit. Index. DC Circuits. HyperPhysics ***** Electricity and Magnetism.

Solve problems in DC circuits Week 3. Take the Series DC Circuits Practice Worksheet with Answers (Basic Electricity) worksheet. These questions & answers will help you master the topic! DC Circuits. A tutorial on how to use Kirchhoff's and Ohm's laws to solve DC circuit problems is presented. Examples with deatiled solutions are included.

To solve the inrush problem, the user can implement a simple external inrush current limiter circuit, comprised of components as shown in Fig. 2. This circuit can control the rate at which the dc/dc input and output capacitors charge. The capacitor, C1, is chosen to provide the appropriate delay to eliminate both current spikes. Hold-up time