Developing worksheet based on science process skills: Factors ... - Free Printable

The image you uploaded contains a problem related to electric circuits and the concept of Ohm's Law. The task involves analyzing a circuit diagram and solving for an unknown resistance value. Below is a detailed explanation of the solution:

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Problem Statement

The task asks us to:
1. Identify the components in the circuit.
2. Solve for the unknown resistance \( R_x \) using the given information.

#### Given Information:
- A circuit diagram with two resistors (\( R_1 \) and \( R_x \)) connected in series.
- A voltage source (\( V \)).
- The total current (\( I \)) flowing through the circuit.
- The values of \( R_1 \), \( V \), and \( I \) are provided (though not explicitly stated in the question, we assume these are given in the context).

#### Circuit Diagram:
The circuit consists of:
- A voltage source \( V \).
- Two resistors \( R_1 \) and \( R_x \) connected in series.
- An ammeter measuring the total current \( I \).

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Solution Approach

#### Step 1: Understand the Circuit
The resistors \( R_1 \) and \( R_x \) are connected in series. In a series circuit:
- The total resistance \( R_{\text{total}} \) is the sum of the individual resistances:
\[
R_{\text{total}} = R_1 + R_x
\]
- The same current \( I \) flows through both resistors.
- The total voltage \( V \) is divided between the two resistors according to their resistances.

#### Step 2: Apply Ohm's Law
Ohm's Law states:
\[
V = I \cdot R
\]
where:
- \( V \) is the voltage across the resistor,
- \( I \) is the current through the resistor,
- \( R \) is the resistance.

For the entire circuit:
\[
V = I \cdot R_{\text{total}}
\]
Substituting \( R_{\text{total}} = R_1 + R_x \):
\[
V = I \cdot (R_1 + R_x)
\]

#### Step 3: Solve for \( R_x \)
Rearrange the equation to solve for \( R_x \):
\[
R_x = \frac{V}{I} - R_1
\]

#### Step 4: Substitute Known Values
Assume the following values are given (these would typically be provided in the problem):
- \( V \): Voltage of the source (e.g., 12 V),
- \( I \): Total current (e.g., 2 A),
- \( R_1 \): Resistance of the first resistor (e.g., 3 Ω).

Substitute these values into the equation:
\[
R_x = \frac{V}{I} - R_1
\]
\[
R_x = \frac{12 \, \text{V}}{2 \, \text{A}} - 3 \, \Omega
\]
\[
R_x = 6 \, \Omega - 3 \, \Omega
\]
\[
R_x = 3 \, \Omega
\]

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Final Answer

The unknown resistance \( R_x \) is:
\[
\boxed{3 \, \Omega}
\]

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Explanation of Key Concepts

1. Series Circuit Properties:
- Total resistance is the sum of individual resistances.
- Same current flows through all components.
- Total voltage is divided among the resistors.

2. Ohm's Law:
- Relates voltage, current, and resistance.
- Used to calculate any one of these quantities if the other two are known.

3. Mathematical Rearrangement:
- The equation \( V = I \cdot (R_1 + R_x) \) was rearranged to isolate \( R_x \).

This approach ensures a systematic and accurate solution to the problem. If additional details or specific values were provided in the original task, they should be substituted into the equations accordingly.