Series-Parallel Circuit Worksheet #3 Answer Key | PDF - Free Printable

It seems you've uploaded an image of a worksheet titled "Series-Parallel Circuit Worksheet #3" with four circuits labeled 1, 2, 3, and 4. The task likely involves analyzing these circuits to determine their equivalent resistance, current, or voltage distribution. Since the image is partially obscured, I'll provide a general explanation of how to solve such problems for series-parallel circuits.

General Approach to Solving Series-Parallel Circuits

1. Identify Series and Parallel Components:
- Series Connection: Resistors are in series if they are connected end-to-end, and the same current flows through each resistor.
- Parallel Connection: Resistors are in parallel if they are connected across the same two points, and the voltage across each resistor is the same.

2. Simplify the Circuit:
- Replace series resistors with their equivalent resistance using the formula:
\[
R_{\text{eq}} = R_1 + R_2 + \cdots + R_n
\]
- Replace parallel resistors with their equivalent resistance using the formula:
\[
\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}
\]

3. Iterate Until Simplified:
- Continue simplifying the circuit by combining series and parallel resistors until you have a single equivalent resistance.

4. Calculate Total Current (if needed):
- Use Ohm's Law:
\[
I = \frac{V}{R_{\text{eq}}}
\]
where \( V \) is the total voltage supplied by the battery.

5. Determine Voltage and Current Distribution:
- For series resistors, the voltage drop across each resistor is proportional to its resistance:
\[
V_i = I \cdot R_i
\]
- For parallel resistors, the current through each resistor is inversely proportional to its resistance:
\[
I_i = \frac{V}{R_i}
\]

Example Solution for Each Circuit Type

#### Circuit 1: Simple Series Circuit
- If all resistors are in series, simply add their resistances:
\[
R_{\text{eq}} = R_1 + R_2 + \cdots + R_n
\]

#### Circuit 2: Simple Parallel Circuit
- If all resistors are in parallel, use the parallel resistance formula:
\[
\frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots + \frac{1}{R_n}
\]

#### Circuit 3: Mixed Series-Parallel Circuit
- Identify which resistors are in series and which are in parallel.
- Simplify the parallel sections first, then combine them with series resistors.
- Repeat until a single equivalent resistance is obtained.

#### Circuit 4: Complex Series-Parallel Circuit
- Follow the same approach as Circuit 3 but with more steps.
- Be careful to identify nested series and parallel combinations.

Example Calculation for a Mixed Circuit

Suppose we have the following mixed circuit:
- Resistors \( R_1 = 10 \, \Omega \), \( R_2 = 20 \, \Omega \), and \( R_3 = 30 \, \Omega \).
- \( R_1 \) and \( R_2 \) are in parallel, and their combination is in series with \( R_3 \).

1. Calculate the equivalent resistance of \( R_1 \) and \( R_2 \):
\[
\frac{1}{R_{\text{eq,1-2}}} = \frac{1}{10} + \frac{1}{20} = \frac{2}{20} + \frac{1}{20} = \frac{3}{20}
\]
\[
R_{\text{eq,1-2}} = \frac{20}{3} \, \Omega \approx 6.67 \, \Omega
\]

2. Add \( R_{\text{eq,1-2}} \) in series with \( R_3 \):
\[
R_{\text{eq}} = R_{\text{eq,1-2}} + R_3 = \frac{20}{3} + 30 = \frac{20}{3} + \frac{90}{3} = \frac{110}{3} \, \Omega \approx 36.67 \, \Omega
\]

Final Answer

The equivalent resistance of the circuit depends on the specific resistances and connections in each circuit. For the example above, the equivalent resistance is:
\[
\boxed{\frac{110}{3} \, \Omega}
\]

If you provide the exact values and configurations from your worksheet, I can solve them specifically!