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Parallel Circuit Worksheet #1, which is designed to help students practice analyzing parallel circuits using Ohm's Law and circuit principles. Since I can't view images directly, I’ll guide you through solving this type of worksheet based on the standard format and content typically found in such worksheets.
Let’s assume the worksheet contains several parallel circuits with resistors, voltage sources, and some known values (like voltage or resistance), and you're asked to calculate missing values like current, resistance, or voltage using Ohm's Law:
>
Ohm’s Law:
> \( V = I \times R \)
> Where:
> - \( V \) = Voltage (Volts)
> - \( I \) = Current (Amperes)
> - \( R \) = Resistance (Ohms)
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General Rules for Parallel Circuits:
1.
Voltage is the same across all branches:
\( V_{\text{total}} = V_1 = V_2 = \dots \)
2.
Total current is the sum of currents in each branch:
\( I_{\text{total}} = I_1 + I_2 + \dots \)
3.
Total resistance is calculated by:
\( \frac{1}{R_{\text{total}}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots \)
Or if two resistors:
\( R_{\text{total}} = \frac{R_1 \times R_2}{R_1 + R_2} \)
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Let’s go through typical problems from such a worksheet.
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Example Problem 1 (Assumed):
Circuit 1:
- Voltage source: 12 V
- Two resistors in parallel: \( R_1 = 6\ \Omega \), \( R_2 = 3\ \Omega \)
- Find: \( I_1 \), \( I_2 \), \( I_{\text{total}} \), \( R_{\text{total}} \)
#### Step-by-step solution:
1.
Voltage across each resistor:
\( V_1 = V_2 = 12\ \text{V} \)
2.
Current through each resistor:
- \( I_1 = \frac{V}{R_1} = \frac{12}{6} = 2\ \text{A} \)
- \( I_2 = \frac{V}{R_2} = \frac{12}{3} = 4\ \text{A} \)
3.
Total current:
- \( I_{\text{total}} = I_1 + I_2 = 2 + 4 = 6\ \text{A} \)
4.
Total resistance:
- \( \frac{1}{R_{\text{total}}} = \frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2} \)
- So, \( R_{\text{total}} = 2\ \Omega \)
5.
Check with Ohm’s Law:
- \( I_{\text{total}} = \frac{V}{R_{\text{total}}} = \frac{12}{2} = 6\ \text{A} \)
✔
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Example Problem 2:
Circuit 2:
- \( R_1 = 4\ \Omega \), \( R_2 = 8\ \Omega \), total current \( I_{\text{total}} = 3\ \text{A} \)
- Find: \( V \), \( I_1 \), \( I_2 \)
#### Solution:
1.
Find total resistance:
\( \frac{1}{R_{\text{total}}} = \frac{1}{4} + \frac{1}{8} = \frac{2}{8} + \frac{1}{8} = \frac{3}{8} \Rightarrow R_{\text{total}} = \frac{8}{3} \approx 2.67\ \Omega \)
2.
Voltage:
\( V = I_{\text{total}} \times R_{\text{total}} = 3 \times \frac{8}{3} = 8\ \text{V} \)
3.
Branch currents:
- \( I_1 = \frac{V}{R_1} = \frac{8}{4} = 2\ \text{A} \)
- \( I_2 = \frac{V}{R_2} = \frac{8}{8} = 1\ \text{A} \)
- Check: \( I_1 + I_2 = 2 + 1 = 3\ \text{A} \)
✔
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Tips for Solving These Problems:
- Always identify what’s given and what’s unknown.
- Use the rules of parallel circuits first.
- Apply Ohm’s Law to each branch and total circuit.
- Double-check your answers by verifying conservation of current and voltage.
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If you can describe the specific values in any of the circuits (e.g., “Problem 1 has a 9V battery and two resistors: 3Ω and 6Ω”), I can walk you through that exact problem step-by-step.
Alternatively, if you can copy-paste the text of one of the problems (like the numbers and layout), I can solve it for you exactly as it appears.
Let me know how you'd like to proceed!
Parent Tip: Review the logic above to help your child master the concept of parallel circuit worksheet.
