Solved PARALLEL CIRCUIT PROBLEMS Use Ohms Law and the rules ... - Free Printable

Let’s solve each problem one by one using the rules for parallel circuits and Ohm’s Law (V = I × R).

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Problem 1:

Two resistors in parallel: R₁ = 10Ω, R₂ = 10Ω.

Formula for total resistance in parallel:
1/Rₜ = 1/R₁ + 1/R₂
→ 1/Rₜ = 1/10 + 1/10 = 2/10 = 1/5
→ So Rₜ = 5Ω

✔ Final Answer for Problem 1: Rₜ = 5Ω

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Problem 2:

Vₜ = 20V, R₁ = 20Ω, R₂ = 20Ω

First, find Rₜ:

1/Rₜ = 1/20 + 1/20 = 2/20 = 1/10 → Rₜ = 10Ω

Now use Ohm’s Law to find Iₜ:
Iₜ = Vₜ / Rₜ = 20V / 10Ω = 2A

✔ Final Answers for Problem 2: Rₜ = 10Ω, Iₜ = 2A

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Problem 3:

Vₜ = 40V, R₁ = 20Ω, Iₜ = 4A (total current)

In a parallel circuit, voltage across each branch is the same as total voltage.

So:
V₁ = Vₜ = 40V
V₂ = Vₜ = 40V

Now find I₁:
I₁ = V₁ / R₁ = 40V / 20Ω = 2A

Total current Iₜ = I₁ + I₂ → 4A = 2A + I₂ → I₂ = 2A

Now find R₂:
R₂ = V₂ / I₂ = 40V / 2A = 20Ω

Find Rₜ:
We can use Ohm’s Law with total values:
Rₜ = Vₜ / Iₜ = 40V / 4A = 10Ω
(Or check: 1/Rₜ = 1/20 + 1/20 = 1/10 → Rₜ = 10Ω — matches!)

✔ Final Answers for Problem 3:
V₁ = 40V, I₁ = 2A, Rₜ = 10Ω
V₂ = 40V, I₂ = 2A, R₂ = 20Ω

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Problem 4:

R₁ = 30Ω, R₂ = 30Ω, Iₜ = 4A

First, find Rₜ:

1/Rₜ = 1/30 + 1/30 = 2/30 = 1/15 → Rₜ = 15Ω

Now find Vₜ using Ohm’s Law:
Vₜ = Iₜ × Rₜ = 4A × 15Ω = 60V

✔ Final Answers for Problem 4: Rₜ = 15Ω, Vₜ = 60V

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Problem 5:

R₁ = 30Ω, R₂ = 30Ω, Iₜ = 2A

Find Rₜ first:

1/Rₜ = 1/30 + 1/30 = 2/30 = 1/15 → Rₜ = 15Ω

Now find Vₜ:
Vₜ = Iₜ × Rₜ = 2A × 15Ω = 30V

In parallel, voltage across each resistor equals total voltage:
V₂ = Vₜ = 30V

✔ Final Answers for Problem 5:
Rₜ = 15Ω, Vₜ = 30V, V₂ = 30V

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Problem 6:

Vₜ = 80V, R₁ = 40Ω, R₂ = 40Ω

Find Rₜ:

1/Rₜ = 1/40 + 1/40 = 2/40 = 1/20 → Rₜ = 20Ω

Find Iₜ:
Iₜ = Vₜ / Rₜ = 80V / 20Ω = 4A

Voltage across each branch equals total voltage:
V₁ = Vₜ = 80V
V₂ = Vₜ = 80V

✔ Final Answers for Problem 6:
Rₜ = 20Ω, Iₜ = 4A
V₁ = 80V, V₂ = 80V

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Final Answer:
Problem 1: Rₜ = 5Ω
Problem 2: Rₜ = 10Ω, Iₜ = 2A
Problem 3: V₁ = 40V, I₁ = 2A, Rₜ = 10Ω; V₂ = 40V, I₂ = 2A, R₂ = 20Ω
Problem 4: Rₜ = 15Ω, Vₜ = 60V
Problem 5: Rₜ = 15Ω, Vₜ = 30V, V₂ = 30V
Problem 6: Rₜ = 20Ω, Iₜ = 4A; V₁ = 80V, V₂ = 80V