Let’s solve each circuit step by step. We’ll use Ohm’s Law:
V = I × R → so
I = V / R, and
R = V / I
We’ll go one box at a time.
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🔹 Top Left Circuit:
Given:
- Battery voltage (V_total) = 12 V
- R₁ = 4 Ω, R₂ = 8 Ω → connected in series
- So total resistance R_total = R₁ + R₂ = 4 + 8 =
12 Ω
- Total current I_total = V_total / R_total = 12 V / 12 Ω =
1 A
In series circuits, current is same everywhere → I₁ = I₂ = I_total =
1 A
Voltage across R₁: V₁ = I₁ × R₁ = 1 A × 4 Ω =
4 V
Voltage across R₂: V₂ = I₂ × R₂ = 1 A × 8 Ω =
8 V
Check: V₁ + V₂ = 4 + 8 = 12 V
✔ matches battery
→ Answers for top left:
- I_total = 1 A
- I₁ = 1 A
- I₂ = 1 A
- V₁ = 4 V
- V₂ = 8 V
---
🔹 Top Right Circuit:
Given:
- Battery = 9 V
- R₁ = 3 Ω, R₂ = 6 Ω → in series
- R_total = 3 + 6 =
9 Ω
- I_total = 9 V / 9 Ω =
1 A
Series → I₁ = I₂ = 1 A
V₁ = 1 A × 3 Ω =
3 V
V₂ = 1 A × 6 Ω =
6 V
Check: 3 + 6 = 9 V
✔
→ Answers for top right:
- I_total = 1 A
- I₁ = 1 A
- I₂ = 1 A
- V₁ = 3 V
- V₂ = 6 V
---
🔹 Middle Left Circuit:
Given:
- Battery = 15 V
- R₁ = 5 Ω, R₂ = 10 Ω → in series
- R_total = 5 + 10 =
15 Ω
- I_total = 15 V / 15 Ω =
1 A
Series → I₁ = I₂ = 1 A
V₁ = 1 × 5 =
5 V
V₂ = 1 × 10 =
10 V
Check: 5 + 10 = 15 V
✔
→ Answers for middle left:
- I_total = 1 A
- I₁ = 1 A
- I₂ = 1 A
- V₁ = 5 V
- V₂ = 10 V
---
🔹 Middle Right Circuit:
Given:
- Battery = 6 V
- R₁ = 2 Ω, R₂ = 4 Ω → in series
- R_total = 2 + 4 =
6 Ω
- I_total = 6 V / 6 Ω =
1 A
Series → I₁ = I₂ = 1 A
V₁ = 1 × 2 =
2 V
V₂ = 1 × 4 =
4 V
Check: 2 + 4 = 6 V
✔
→ Answers for middle right:
- I_total = 1 A
- I₁ = 1 A
- I₂ = 1 A
- V₁ = 2 V
- V₂ = 4 V
---
🔹 Bottom Left Circuit:
Given:
- Battery = 18 V
- R₁ = 6 Ω, R₂ = 12 Ω → in series
- R_total = 6 + 12 =
18 Ω
- I_total = 18 V / 18 Ω =
1 A
Series → I₁ = I₂ = 1 A
V₁ = 1 × 6 =
6 V
V₂ = 1 × 12 =
12 V
Check: 6 + 12 = 18 V
✔
→ Answers for bottom left:
- I_total = 1 A
- I₁ = 1 A
- I₂ = 1 A
- V₁ = 6 V
- V₂ = 12 V
---
🔹 Bottom Right Circuit:
Given:
- Battery = 24 V
- R₁ = 8 Ω, R₂ = 16 Ω → in series
- R_total = 8 + 16 =
24 Ω
- I_total = 24 V / 24 Ω =
1 A
Series → I₁ = I₂ = 1 A
V₁ = 1 × 8 =
8 V
V₂ = 1 × 16 =
16 V
Check: 8 + 16 = 24 V
✔
→ Answers for bottom right:
- I_total = 1 A
- I₁ = 1 A
- I₂ = 1 A
- V₁ = 8 V
- V₂ = 16 V
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✔ All circuits follow the same pattern: two resistors in series with a battery. Total resistance adds up, current is same through both, voltages add to battery voltage.
Final Answer:
Top Left:
I_total = 1 A, I₁ = 1 A, I₂ = 1 A, V₁ = 4 V, V₂ = 8 V
Top Right:
I_total = 1 A, I₁ = 1 A, I₂ = 1 A, V₁ = 3 V, V₂ = 6 V
Middle Left:
I_total = 1 A, I₁ = 1 A, I₂ = 1 A, V₁ = 5 V, V₂ = 10 V
Middle Right:
I_total = 1 A, I₁ = 1 A, I₂ = 1 A, V₁ = 2 V, V₂ = 4 V
Bottom Left:
I_total = 1 A, I₁ = 1 A, I₂ = 1 A, V₁ = 6 V, V₂ = 12 V
Bottom Right:
I_total = 1 A, I₁ = 1 A, I₂ = 1 A, V₁ = 8 V, V₂ = 16 V
Parent Tip: Review the logic above to help your child master the concept of series circuit problems worksheet.
