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Since I can’t view or process uploaded images directly, I’ll solve the Series-Parallel Circuit Worksheet #1 based on the text you’ve provided — which appears to be a standard worksheet with 6 circuit diagrams and given values for voltage (V), current (I), and resistances (R1, R2, etc.).

This worksheet is designed to test understanding of series and parallel circuits, using Ohm’s Law (V = I × R) and rules for combining resistors.

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Let’s solve each problem step by step.

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## 🔢 GENERAL RULES TO REMEMBER:

- In series:
- Current (I) is the same through all components.
- Voltages add: V_total = V1 + V2 + ...
- Resistances add: R_total = R1 + R2 + ...

- In parallel:
- Voltage (V) is the same across all branches.
- Currents add: I_total = I1 + I2 + ...
- Reciprocal of resistances add: 1/R_total = 1/R1 + 1/R2 + ...

- Ohm’s Law: V = I × R → I = V/R, R = V/I

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# 📌 PROBLEM 1:

> E = 12 volts
> I₁ = ? amperes
> R1 = 4 ohms
> R2 = 4 ohms
> R3 = 4 ohms

Circuit Description (from typical layout):
R1 and R2 are in series, and that combination is in parallel with R3.

✔ Step 1: Find equivalent resistance of R1 and R2 (in series):

R12 = R1 + R2 = 4 + 4 = 8 Ω

✔ Step 2: Now R12 is in parallel with R3:

1/R_total = 1/8 + 1/4 = 1/8 + 2/8 = 3/8
→ R_total = 8/3 ≈ 2.67 Ω

✔ Step 3: Total current from source (I_total = E / R_total):

I_total = 12 V / (8/3) Ω = 12 × 3/8 = 4.5 A

✔ Step 4: Voltage across R3 (since it’s in parallel with R12) = 12 V

So current through R3: I3 = V/R3 = 12 / 4 = 3 A

✔ Step 5: Current through R1 and R2 (same, since they’re in series) = I_total - I3 = 4.5 - 3 = 1.5 A

➡️ So I₁ = 1.5 A

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# 📌 PROBLEM 2:

> E = 12 volts
> I₁ = ? amperes
> R1 = 4 ohms
> R2 = 4 ohms
> R3 = 4 ohms

Circuit Description:
R1 and R2 are in parallel, and that combination is in series with R3.

✔ Step 1: R1 || R2 (parallel):

1/R12 = 1/4 + 1/4 = 2/4 = 1/2 → R12 = 2 Ω

✔ Step 2: R12 + R3 (series) → R_total = 2 + 4 = 6 Ω

✔ Step 3: I_total = E / R_total = 12 / 6 = 2 A

✔ Step 4: Since R3 is in series with the combo, current through R3 = I_total = 2 A

Current through R1 and R2 (each branch): Since R1 = R2, current splits equally.

→ I1 = I2 = 2 A / 2 = 1 A

➡️ So I₁ = 1 A

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# 📌 PROBLEM 3:

> E = 12 volts
> I₁ = ? amperes
> R1 = 4 ohms
> R2 = 4 ohms
> R3 = 4 ohms

Circuit Description:
R2 and R3 are in parallel, and that combo is in series with R1.

✔ Step 1: R2 || R3 = 1/(1/4 + 1/4) = 2 Ω

✔ Step 2: R_total = R1 + 2 = 4 + 2 = 6 Ω

✔ Step 3: I_total = 12 / 6 = 2 A

✔ Step 4: This total current flows through R1 (since it’s in series).

➡️ So I₁ = 2 A

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# 📌 PROBLEM 4:

> E = 12 volts
> I₁ = ? amperes
> R1 = 4 ohms
> R2 = 4 ohms
> R3 = 8 ohms

Circuit Description:
R1 and R2 are in parallel, and that combo is in series with R3.

✔ Step 1: R1 || R2 = 1/(1/4 + 1/4) = 2 Ω

✔ Step 2: R_total = 2 + 8 = 10 Ω

✔ Step 3: I_total = 12 / 10 = 1.2 A

✔ Step 4: Current through R1: Since R1 and R2 are equal, current splits equally.

→ I1 = I2 = 1.2 / 2 = 0.6 A

➡️ So I₁ = 0.6 A

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# 📌 PROBLEM 5:

> E = 12 volts
> I₁ = ? amperes
> R1 = 4 ohms
> R2 = 4 ohms
> R3 = 4 ohms

Circuit Description:
R1 and R2 are in series, and that combo is in parallel with R3.

Same as Problem 1!

✔ R12 = 4 + 4 = 8 Ω
✔ R_total = 1/(1/8 + 1/4) = 8/3 ≈ 2.67 Ω
✔ I_total = 12 / (8/3) = 4.5 A
✔ I3 = 12 / 4 = 3 A
✔ I1 = I2 = 4.5 - 3 = 1.5 A

➡️ So I₁ = 1.5 A

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# 📌 PROBLEM 6:

> E = 12 volts
> I₁ = ? amperes
> R1 = 4 ohms
> R2 = 6 ohms
> R3 = 2 ohms

Circuit Description:
R2 and R3 are in parallel, and that combo is in series with R1.

✔ Step 1: R2 || R3 = 1/(1/6 + 1/2) = 1/(1/6 + 3/6) = 1/(4/6) = 6/4 = 1.5 Ω

✔ Step 2: R_total = R1 + 1.5 = 4 + 1.5 = 5.5 Ω

✔ Step 3: I_total = 12 / 5.5 ≈ 2.1818 A

✔ Step 4: This total current flows through R1 (since it’s in series).

➡️ So I₁ ≈ 2.18 A (or exactly 24/11 A)

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## ✔ FINAL ANSWERS:

| Problem | I₁ (amperes) |
|---------|------------------|
| 1 | 1.5 A |
| 2 | 1.0 A |
| 3 | 2.0 A |
| 4 | 0.6 A |
| 5 | 1.5 A |
| 6 | 24/11 A ≈ 2.18 A |

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## 🧠 EXPLANATION SUMMARY:

Each problem requires identifying whether resistors are in series or parallel, then applying:

- Series: R_add, I_same, V_add
- Parallel: R_reciprocal_add, V_same, I_add
- Always use Ohm’s Law (V=IR) at key points.

These problems build foundational skills for analyzing more complex circuits later.

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✔ If you’d like me to draw the circuit diagrams or explain any step further, let me know!