Collection of electrical circuit problems involving parallel resistors, voltage sources, and current calculations.

Let’s solve each circuit problem one by one. All circuits shown are parallel circuits, so we’ll use the rules for parallel circuits:

- Voltage is the same across all branches:
→ V₁ = V₂ = Vₜ (total voltage)

- Total resistance (Rₜ) in parallel:
→ 1/Rₜ = 1/R₁ + 1/R₂ + ...
→ Rₜ = 1 / (sum of reciprocals)

- Current through each branch: I = V / R
- Total current: Iₜ = I₁ + I₂ + ...

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Problem 7:

Given:
Vₜ = 6V, R₁ = 3Ω, R₂ = 6Ω

Since it’s parallel:
→ V₁ = V₂ = Vₜ = 6V

Currents:
I₁ = V₁ / R₁ = 6V / 3Ω = 2A
I₂ = V₂ / R₂ = 6V / 6Ω = 1A

Total current:
Iₜ = I₁ + I₂ = 2A + 1A = 3A

Total resistance:
1/Rₜ = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2
→ Rₜ = 2Ω

✔ Check: Vₜ = Iₜ × Rₜ → 3A × 2Ω = 6V ✔️

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Problem 8:

Given:
Vₜ = 40V, R₁ = 5Ω, R₂ = 20Ω

Parallel → V₁ = V₂ = 40V

Currents:
I₁ = 40V / 5Ω = 8A
I₂ = 40V / 20Ω = 2A

Total current:
Iₜ = 8A + 2A = 10A

Total resistance:
1/Rₜ = 1/5 + 1/20 = 4/20 + 1/20 = 5/20 = 1/4
→ Rₜ = 4Ω

✔ Check: 10A × 4Ω = 40V ✔️

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Problem 9:

Given:
Iₜ = 3A, R₁ = 24Ω, R₂ = 48Ω

First, find Rₜ:
1/Rₜ = 1/24 + 1/48 = 2/48 + 1/48 = 3/48 = 1/16
→ Rₜ = 16Ω

Now, Vₜ = Iₜ × Rₜ = 3A × 16Ω = 48V

In parallel: V₁ = V₂ = Vₜ = 48V

Currents:
I₁ = 48V / 24Ω = 2A
I₂ = 48V / 48Ω = 1A

✔ Check: I₁ + I₂ = 2A + 1A = 3A = Iₜ ✔️

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Problem 10:

Given:
Iₜ = 3A, R₁ = 6Ω, R₂ = 12Ω

Find Rₜ:
1/Rₜ = 1/6 + 1/12 = 2/12 + 1/12 = 3/12 = 1/4
→ Rₜ = 4Ω

Vₜ = Iₜ × Rₜ = 3A × 4Ω = 12V

Parallel → V₁ = V₂ = 12V

Currents:
I₁ = 12V / 6Ω = 2A
I₂ = 12V / 12Ω = 1A

✔ Check: 2A + 1A = 3A ✔️

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Problem 11:

Given:
Vₜ = 40V, R₁ = 10Ω, Iₜ = 5A

We need to find R₂? Wait — actually, the diagram shows R₂ but no value given. But we can find it using total current.

First, since parallel:
V₁ = V₂ = Vₜ = 40V

I₁ = V₁ / R₁ = 40V / 10Ω = 4A

Iₜ = I₁ + I₂ → 5A = 4A + I₂ → I₂ = 1A

Then R₂ = V₂ / I₂ = 40V / 1A = 40Ω

But the question doesn’t ask for R₂ — it asks for V₁, V₂, I₁, I₂.

So:
V₁ = 40V, V₂ = 40V
I₁ = 4A, I₂ = 1A

✔ Check: I₁ + I₂ = 5A ✔️

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Problem 12:

Given:
Vₜ = 24V, R₁ = 12Ω, R₂ = 24Ω

Parallel → V₁ = V₂ = 24V

Currents:
I₁ = 24V / 12Ω = 2A
I₂ = 24V / 24Ω = 1A

Total current:
Iₜ = 2A + 1A = 3A

Total resistance:
1/Rₜ = 1/12 + 1/24 = 2/24 + 1/24 = 3/24 = 1/8
→ Rₜ = 8Ω

✔ Check: 3A × 8Ω = 24V ✔️

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Problem 13:

Three resistors in parallel: 5Ω, 20Ω, 4Ω

Find Rₜ:

1/Rₜ = 1/5 + 1/20 + 1/4

Convert to 20ths:
= 4/20 + 1/20 + 5/20 = 10/20 = 1/2
→ Rₜ = 2Ω

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Problem 14:

Three resistors: 48Ω, 16Ω, 24Ω

1/Rₜ = 1/48 + 1/16 + 1/24

Common denominator = 48:
= 1/48 + 3/48 + 2/48 = 6/48 = 1/8
→ Rₜ = 8Ω

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Final Answers:

Problem 7:
V₁ = 6V, I₁ = 2A, I₂ = 1A, Iₜ = 3A, V₂ = 6V, Rₜ = 2Ω

Problem 8:
Rₜ = 4Ω, I₁ = 8A, I₂ = 2A, Iₜ = 10A

Problem 9:
Rₜ = 16Ω, Vₜ = 48V, V₁ = 48V, I₁ = 2A, V₂ = 48V, I₂ = 1A

Problem 10:
Rₜ = 4Ω, Vₜ = 12V, V₁ = 12V, V₂ = 12V, I₂ = 1A, I₁ = 2A

Problem 11:
V₁ = 40V, V₂ = 40V, I₁ = 4A, I₂ = 1A

Problem 12:
V₁ = 24V, I₁ = 2A, V₂ = 24V, I₂ = 1A, Iₜ = 3A, Rₜ = 8Ω

Problem 13:
Rₜ = 2Ω

Problem 14:
Rₜ = 8Ω

Final Answer:
Problem 7: V₁=6V, I₁=2A, I₂=1A, Iₜ=3A, V₂=6V, Rₜ=2Ω
Problem 8: Rₜ=4Ω, I₁=8A, I₂=2A, Iₜ=10A
Problem 9: Rₜ=16Ω, Vₜ=48V, V₁=48V, I₁=2A, V₂=48V, I₂=1A
Problem 10: Rₜ=4Ω, Vₜ=12V, V₁=12V, V₂=12V, I₂=1A, I₁=2A
Problem 11: V₁=40V, V₂=40V, I₁=4A, I₂=1A
Problem 12: V₁=24V, I₁=2A, V₂=24V, I₂=1A, Iₜ=3A, Rₜ=8Ω
Problem 13: Rₜ=2Ω
Problem 14: Rₜ=8Ω