Worksheet on parallel circuit problems with diagrams and calculations for voltage, current, and resistance.

Let’s solve each of the 6 parallel circuit problems step by step. We’ll use these key rules for parallel circuits:

✔ Voltage is the same across all branches → V₁ = V₂ = Vₜ
✔ Total current adds up → Iₜ = I₁ + I₂ (or more if more branches)
✔ For total resistance: 1/Rₜ = 1/R₁ + 1/R₂ + ... then flip it to get Rₜ
✔ Ohm’s Law: V = I × R → so I = V/R and R = V/I

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Problem 1 (Top Left):

Given:
- Battery voltage? Not given directly — but we see ammeters showing currents.
Wait — actually, looking at the diagram: there’s a battery with “2A” next to it? That might be total current.
But also resistors: R₁ = 12Ω, R₂ = 24Ω

Actually — let me re-read the diagram carefully.

In top-left box:
- There’s a battery symbol on left.
- Two resistors in parallel: R₁=12Ω, R₂=24Ω
- An ammeter labeled “2A” is placed in series with the battery → that means total current Iₜ = 2A
- We need to find: Rₑq, Vₜ, V₁, V₂, I₁, I₂

Step 1: Find equivalent resistance Rₑq

1/Rₑq = 1/12 + 1/24
→ Common denominator 24: 2/24 + 1/24 = 3/24 = 1/8
→ So Rₑq = 8 Ω

Step 2: Use Ohm’s Law to find total voltage Vₜ
Vₜ = Iₜ × Rₑq = 2A × 8Ω = 16V

Since it’s parallel: V₁ = V₂ = Vₜ = 16V

Step 3: Find branch currents
I₁ = V₁ / R₁ = 16V / 12Ω ≈ 1.333 A
I₂ = V₂ / R₂ = 16V / 24Ω ≈ 0.667 A

Check: I₁ + I₂ = 1.333 + 0.667 = 2A → matches Iₜ ✔

So answers for Problem 1:
Rₑq = 8Ω
Vₜ = 16V
V₁ = 16V
V₂ = 16V
I₁ = 1.33A (or 4/3 A)
I₂ = 0.67A (or 2/3 A)

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Problem 2 (Top Right):

Diagram shows:
- Ammeter labeled “4a” → probably 4A total current? But wait — it's drawn above the junction, likely measuring total current entering the parallel part.
Resistors: R₁ = 20Ω, R₂ = 20Ω

Assume Iₜ = 4A (from ammeter label)

Step 1: Rₑq for two equal resistors in parallel:
Rₑq = R/2 = 20/2 = 10Ω

Step 2: Vₜ = Iₜ × Rₑq = 4A × 10Ω = 40V

Then V₁ = V₂ = 40V

Step 3: I₁ = V₁/R₁ = 40/20 = 2A
I₂ = 40/20 = 2A

Check: 2+2=4A → correct.

Answers:
Rₑq = 10Ω
Iₜ = 4A (given)
Vₜ = 40V
V₁ = 40V
V₂ = 40V
I₁ = 2A
I₂ = 2A

(Note: The worksheet has blanks like “R_eq = ___”, “I_t = ___”, etc. — we fill them.)

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Problem 3 (Middle Left):

Battery labeled “6v” → so Vₜ = 6V
Two ammeters: one says “2a” over R₁ branch → I₁ = 2A
Other says “1a” over R₂ branch → I₂ = 1A

We need to find: R₁, R₂, Rₑq, Iₜ, V₁, V₂

First: Since parallel, V₁ = V₂ = Vₜ = 6V

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

Now find resistances:

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

Rₑq: 1/Rₑq = 1/3 + 1/6 = 2/6 + 1/6 = 3/6 = 1/2 → Rₑq = 2Ω

Check: Vₜ = Iₜ × Rₑq = 3A × 2Ω = 6V → correct.

Answers:
V₁ = 6V
V₂ = 6V
R₁ = 3Ω
R₂ = 6Ω
Rₑq = 2Ω
Iₜ = 3A
I₁ = 2A (given)
I₂ = 1A (given)

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Problem 4 (Middle Right):

Battery labeled “40v” → Vₜ = 40V
Three resistors: R₁ = 5Ω, R₂ = 20Ω, R₃ = 4Ω

Find: Rₑq, Iₜ, V₁, V₂, V₃, I₁, I₂, I₃

All voltages same: V₁ = V₂ = V₃ = 40V

Currents:

I₁ = V/R₁ = 40/5 = 8A
I₂ = 40/20 = 2A
I₃ = 40/4 = 10A

Total current Iₜ = 8 + 2 + 10 = 20A

Equivalent resistance:

1/Rₑq = 1/5 + 1/20 + 1/4
Convert to twentieths: 4/20 + 1/20 + 5/20 = 10/20 = 1/2
→ Rₑq = 2Ω

Check: V = I×R → 20A × 2Ω = 40V → correct.

Answers:
Rₑq = 2Ω
Iₜ = 20A
V₁ = 40V
V₂ = 40V
V₃ = 40V
I₁ = 8A
I₂ = 2A
I₃ = 10A

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Problem 5 (Bottom Left):

Battery labeled “12v” → Vₜ = 12V
Ammeter labeled “3a” → this is in the main line before splitting → so Iₜ = 3A
Resistor R₁ = 12Ω, R₂ = ? (unknown)

Need to find: V₁, V₂, I₁, I₂, R₂, Rₑq

Voltages: V₁ = V₂ = Vₜ = 12V

I₁ = V₁ / R₁ = 12V / 12Ω = 1A

Since Iₜ = I₁ + I₂ → 3A = 1A + I₂ → I₂ = 2A

Then R₂ = V₂ / I₂ = 12V / 2A = 6Ω

Rₑq = Vₜ / Iₜ = 12V / 3A = 4Ω

Check via formula: 1/Rₑq = 1/12 + 1/6 = 1/12 + 2/12 = 3/12 = 1/4 → Rₑq = 4Ω ✔

Answers:
V₁ = 12V
V₂ = 12V
I₁ = 1A
I₂ = 2A
R₂ = 6Ω
Rₑq = 4Ω

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Problem 6 (Bottom Right):

Battery not labeled with voltage — but resistor R₂ = 15Ω has an ammeter labeled “20v”? Wait — no, look again.

Actually, the ammeter is labeled “20v”? That doesn’t make sense — ammeters measure current, voltmeters measure voltage.

Looking closely: In bottom-right diagram, there’s a circle with “20v” inside, connected across R₂ — that must be a voltmeter, meaning V₂ = 20V.

Also, R₁ = 10Ω, R₂ = 15Ω

Since parallel: V₁ = V₂ = Vₜ = 20V

Now find currents:

I₁ = V₁ / R₁ = 20V / 10Ω = 2A
I₂ = V₂ / R₂ = 20V / 15Ω ≈ 1.333 A (or 4/3 A)

Total current Iₜ = I₁ + I₂ = 2 + 1.333 = 3.333 A (or 10/3 A)

Rₑq: 1/Rₑq = 1/10 + 1/15
LCM of 10 and 15 is 30 → 3/30 + 2/30 = 5/30 = 1/6 → Rₑq = 6Ω

Check: V = I×R → (10/3)A × 6Ω = 60/3 = 20V → correct.

Answers:
V₁ = 20V
V₂ = 20V
I₁ = 2A
I₂ = 1.33A (or 4/3 A)
Rₑq = 6Ω
Iₜ = 3.33A (or 10/3 A)

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Now, compiling final answers per problem as requested by worksheet format.

Note: Some values are fractions — we can write decimals rounded to 2 places or exact fractions. Since it’s school level, decimals are fine unless specified.

Let’s list each problem’s required fills:

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Final Answer:

Problem 1 (Top Left):
Rₑq = 8 Ω
Iₜ = 2 A
Vₜ = 16 V
V₁ = 16 V
V₂ = 16 V
I₁ = 1.33 A
I₂ = 0.67 A

Problem 2 (Top Right):
Rₑq = 10 Ω
Iₜ = 4 A
Vₜ = 40 V
V₁ = 40 V
V₂ = 40 V
I₁ = 2 A
I₂ = 2 A

Problem 3 (Middle Left):
V₁ = 6 V
V₂ = 6 V
R₁ = 3 Ω
R₂ = 6 Ω
Rₑq = 2 Ω
Iₜ = 3 A
I₁ = 2 A
I₂ = 1 A

Problem 4 (Middle Right):
Rₑq = 2 Ω
Iₜ = 20 A
V₁ = 40 V
V₂ = 40 V
V₃ = 40 V
I₁ = 8 A
I₂ = 2 A
I₃ = 10 A

Problem 5 (Bottom Left):
V₁ = 12 V
V₂ = 12 V
I₁ = 1 A
I₂ = 2 A
R₂ = 6 Ω
Rₑq = 4 Ω

Problem 6 (Bottom Right):
V₁ = 20 V
V₂ = 20 V
I₁ = 2 A
I₂ = 1.33 A
Rₑq = 6 Ω
Iₜ = 3.33 A

*(Note: Where applicable, fractional forms are acceptable too — e.g., I₂ in Problem 6 = 4/3 A, Iₜ = 10/3 A)*