## Solving DC Circuits

I guess you’re still recovering from an awesome lunches and dinners you’ve had during holidays. Well, now when it’s over – it’s a good moment to plug yourself back and shake your brain cells!

Assuming that you’re very familiar with electric circuits theorems, I advice you to get yourself a good old black coffee and give your brain a training by solving few simple dc circuits :)

**Let’s start.**

### Circuit #1

Using the current division rule, calculate I_{1} and I_{2}, I being **10 A**. Verify the solution, calculating U_{AB} as R_{eqp}I and observing that **R _{1}I_{1} = R_{2}I_{2} = U_{AB}**.

### Circuit #2

**Determine I and U _{AB}.** 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

### Circuit #3

Calculate the **resistance R _{G}** seen by the generator, and

**I**. Then, using the voltage division rule,

_{1}**calculate I**. Check the conservation of power, comparing what is delivered by the generator and what is absorbed by resistors.

_{2}and I_{3}- U
_{s}= 12V - R
_{1}= R_{2}= 2Ω - R
_{3}= 8Ω - R
_{4}= 6Ω

### Circuit #4

By applying Thévenin’s theorem between A and B, calculate the **equivalent voltage U _{Th}** and the

**equivalent resistance R**:

_{Th}### Circuit #5

**Solve the following circuit by using:**

- The superposition rule;
- KCE;
- Nodal analysis to calculate U
_{AB}; - Thévenin’s theorem to find an equivalent, left-side or right-side section AB.

Input circuit parameters:

- U
_{s1}= 12V - R
_{1}= 0.5Ω - R
_{2}= 5Ω - U
_{s2}= 9V

### Circuit #6

**Solve the following circuit by using:**

- The superposition rule;
- KCE;
- Nodal analysis to calculate U
_{AB}(write KCL at node A); - Thévenin’s theorem to find an equivalent, left-side section AB.

Input circuit parameters:

- U
_{s}= 100V - R
_{1}= 20Ω - R
_{2}= 30Ω - I
_{s}= 3A

### Circuit #7

Find at least three ways to calculate **I _{2} and I_{3}**. Is

**R**really required to determine currents? And to calculate the power delivered by

_{1}**I**?

_{S1}- I
_{s1}= 5A - I
_{s2}= 1A - I
_{s3}= 8A - R
_{1}= 5Ω - R
_{2}= 1Ω - R
_{3}= 4Ω

### Circuit #8

Calculate **current I** in the following circuit:

- U
_{s1}= 6V - U
_{s2}= 2V - R
_{1}= 1Ω - R
_{2}= R_{3}= 2Ω - I
_{s}= 3A

### Circuit #9

**Calculate the Thévenin equivalent of the following circuit:**

- U
_{s1}= 6V - U
_{s2}= 2V - R
_{1}= 4Ω - R
_{2}= 6Ω - R
_{3}= 2Ω - R
_{4}= 1Ω - I
_{s}= 1A

### Circuit #10

Calculate **I _{A} and U_{AB}** and determine the power flowing through section AB. Verify the result using the principle of power conservation.

- U
_{s1}= 10V - U
_{s2}= 4V - R
_{1}= 1Ω - R
_{2}= 2Ω - R
_{I}= 1Ω - I
_{s}= 1A

## Circuit Solutions

### Solution #1

- I
_{1}= 7.5A - I
_{2}= 2.5A

### Solution #2

- I = 0.5A
- U
_{AB}= 5V - U
_{s1}charges U_{s2}

### Solution #3

- R
_{G}= 6Ω - I
_{1}= 2A - I
_{2}= I_{3}= 1A

### Solution #4

- U
_{Th}= 6V, R_{Th}= 1.333Ω - U
_{Th}= 5V, R_{Th}= 5Ω - U
_{Th}= 2V, R_{Th}= 4Ω

### Solution #5

- I
_{1}= 6A - I
_{2}= 1.8A - I
_{3}= 4.2A

### Solution #6

- I
_{1}= 0.2A, - I
_{2}= 3.2A

### Solution #7

- I
_{2}= 9.6A - I
_{3}= 2.4A

### Solution #8

I = 2.5A

### Solution #9

- U
_{Th}= 7V - R
_{Th}= 4Ω

### Solution #10

P = 20.22W

### Literature for studying:

#### Basic AC/DC circuit theory, analysis and problems

Theory and problems – Basic circuit analysis by John O’Malley, professor of Electrical Engineering University of Florida.

#### Lessons In DC Electrical Circuits

Lessons In DC Electrical Circuits by Tony R. Kuphaldt.

**Reference //** Fundamentals of electrical engineering by Massimo Ceraolo and Davide Poli (Get yourself hardcover from Amazon)