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# Solve These Ten DC Circuits and Train Your Brain!

Home / Technical Articles / Solve These Ten DC Circuits and Train Your Brain!

## 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 I1 and I2, I being 10 A. Verify the solution, calculating UAB as ReqpI and observing that R1I1 = R2I2 = UAB.

See solution ↓

### Circuit #2

Determine I and UAB. If Us1 and Us2 represent two ideal batteries, which one charges the other?

• Us1 = 120V
• Us2 = 90V
• R1 = R2 = 10Ω
• R3 = 40Ω

See solution ↓

### Circuit #3

Calculate the resistance RG seen by the generator, and I1. Then, using the voltage division rule, calculate I2 and I3. Check the conservation of power, comparing what is delivered by the generator and what is absorbed by resistors.

• Us = 12V
• R1 = R2 = 2Ω
• R3 = 8Ω
• R4 = 6Ω

See solution ↓

### Circuit #4

By applying Thévenin’s theorem between A and B, calculate the equivalent voltage UTh and the equivalent resistance RTh:

See solution ↓

### Circuit #5

Solve the following circuit by using:

1. The superposition rule;
2. KCE;
3. Nodal analysis to calculate UAB;
4. Thévenin’s theorem to find an equivalent, left-side or right-side section AB.

Input circuit parameters:

• Us1 = 12V
• R1 = 0.5Ω
• R2 = 5Ω
• Us2 = 9V

See solution ↓

### Circuit #6

Solve the following circuit by using:

1. The superposition rule;
2. KCE;
3. Nodal analysis to calculate UAB (write KCL at node A);
4. Thévenin’s theorem to find an equivalent, left-side section AB.

Input circuit parameters:

• Us = 100V
• R1 = 20Ω
• R2 = 30Ω
• Is = 3A

See solution ↓

### Circuit #7

Find at least three ways to calculate I2 and I3. Is R1 really required to determine currents? And to calculate the power delivered by IS1?

• Is1 = 5A
• Is2 = 1A
• Is3 = 8A
• R1 = 5Ω
• R2 = 1Ω
• R3 = 4Ω

See solution ↓

### Circuit #8

Calculate current I in the following circuit:

• Us1 = 6V
• Us2 = 2V
• R1 = 1Ω
• R2 = R3 = 2Ω
• Is = 3A

See solution ↓

### Circuit #9

Calculate the Thévenin equivalent of the following circuit:

• Us1 = 6V
• Us2 = 2V
• R1 = 4Ω
• R2 = 6Ω
• R3 = 2Ω
• R4 = 1Ω
• Is = 1A

See solution ↓

### Circuit #10

Calculate IA and UAB and determine the power flowing through section AB. Verify the result using the principle of power conservation.

• Us1 = 10V
• Us2 = 4V
• R1 = 1Ω
• R2 = 2Ω
• RI = 1Ω
• Is = 1A

See solution ↓

## Circuit Solutions

### Solution #1

• I1 = 7.5A
• I2 = 2.5A

Go back to circuit ↑

### Solution #2

• I = 0.5A
• UAB = 5V
• Us1 charges Us2

Go back to circuit ↑

### Solution #3

• RG = 6Ω
• I1 = 2A
• I2 = I3 = 1A

Go back to circuit ↑

### Solution #4

1. UTh = 6V, RTh = 1.333Ω
2. UTh = 5V, RTh = 5Ω
3. UTh = 2V, RTh = 4Ω

Go back to circuit ↑

### Solution #5

• I1 = 6A
• I2 = 1.8A
• I3 = 4.2A

Go back to circuit ↑

### Solution #6

• I1 = 0.2A,
• I2 = 3.2A

Go back to circuit ↑

### Solution #7

• I2 = 9.6A
• I3 = 2.4A

Go back to circuit ↑

### Solution #8

I = 2.5A

Go back to circuit ↑

### Solution #9

• UTh = 7V
• RTh = 4Ω

Go back to circuit ↑

### Solution #10

P = 20.22W

Go back to circuit ↑

### 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)

Get access to premium HV/MV/LV technical articles, electrical engineering guides, research studies and much more! It helps you to shape up your technical skills in your everyday life as an electrical engineer. ### Edvard Csanyi

Electrical engineer, programmer and founder of EEP. Highly specialized for design of LV/MV switchgears and LV high power busbar trunking (<6300A) in power substations, commercial buildings and industry facilities. Professional in AutoCAD programming.

### One Comment

1. Dinesh joun
Apr 07, 2019

Any electrical relationship