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 U_AB as R_eqpI and observing that R₁I₁ = R₂I₂ = U_AB.

See solution ↓

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
• R₁ = R₂ = 10Ω
• R₃ = 40Ω

See solution ↓

Circuit #3

Calculate the resistance R_G 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.

• U_s = 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 U_Th and the equivalent resistance R_Th:

See solution ↓

Circuit #5

Solve the following circuit by using:

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

Input circuit parameters:

• U_s1 = 12V
• R₁ = 0.5Ω
• R₂ = 5Ω
• U_s2 = 9V

See solution ↓

Circuit #6

Solve the following circuit by using:

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

Input circuit parameters:

• U_s = 100V
• R₁ = 20Ω
• R₂ = 30Ω
• I_s = 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 I_S1?

• I_s1 = 5A
• I_s2 = 1A
• I_s3 = 8A
• R₁ = 5Ω
• R₂ = 1Ω
• R₃ = 4Ω

See solution ↓

Circuit #8

Calculate current I in the following circuit:

• U_s1 = 6V
• U_s2 = 2V
• R₁ = 1Ω
• R₂ = R₃ = 2Ω
• I_s = 3A

See solution ↓

Circuit #9

Calculate the Thévenin equivalent of the following circuit:

• U_s1 = 6V
• U_s2 = 2V
• R₁ = 4Ω
• R₂ = 6Ω
• R₃ = 2Ω
• R₄ = 1Ω
• I_s = 1A

See solution ↓

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
• R₁ = 1Ω
• R₂ = 2Ω
• R_I = 1Ω
• I_s = 1A

See solution ↓

Circuit Solutions

Solution #1

• I₁ = 7.5A
• I₂ = 2.5A

Go back to circuit ↑

Solution #2

• I = 0.5A
• U_AB = 5V
• U_s1 charges U_s2

Go back to circuit ↑

Solution #3

• R_G = 6Ω
• I₁ = 2A
• I₂ = I₃ = 1A

Go back to circuit ↑

Solution #4

1. U_Th = 6V, R_Th = 1.333Ω
2. U_Th = 5V, R_Th = 5Ω
3. U_Th = 2V, R_Th = 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

• U_Th = 7V
• R_Th = 4Ω

Go back to circuit ↑

Solution #10

P = 20.22W

Go back to circuit ↑

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