Delmar's Standard Textbook Of Electricity
7th Edition
ISBN: 9781337900348
Author: Stephen L. Herman
Publisher: Cengage Learning
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Determine the value of the current i in the circuit. Current division should be used
![**Problem Statement:**
3. Determine the value of the current \( i \) in the circuit. Current division should be used.
**Circuit Diagram Description:**
- The circuit diagram shows three parallel paths.
- The first path has a 2A current source in series with a 12Ω resistor.
- The second path has a 0.5A current source in series with a 3Ω resistor.
- The third path has a 1.5A current source in series with a 6Ω resistor.
**Explanation:**
This problem involves calculating the current \( i \) through one of the resistors (not labeled in the diagram provided) using the concept of current division. Current division is applicable when you have parallel branches in a circuit, allowing you to determine how current divides among the parallel branches based on their resistance values. In this setup, each path has a specified resistance and a current source.
To solve such a problem, you use the formula for current division:
\[
i_x = \frac{I_{\text{total}} \cdot R_{\text{total}}}{R_x}
\]
Where:
- \( i_x \) is the current through the resistor in question.
- \( I_{\text{total}} \) is the total current supplied to the parallel network.
- \( R_{\text{total}} \) is the total resistance of the parallel network.
- \( R_x \) is the resistance through which you want to find the current.
Since full values aren't given, you will need to apply the concept ideally utilizing the data and conditions provided in the diagram.](https://content.bartleby.com/qna-images/question/ad16e748-6a7d-4448-b034-0f7e391345fb/2273a55d-f828-4fa7-ae32-1f46cd02c46c/82ndit_processed.jpeg)
Transcribed Image Text:**Problem Statement:**
3. Determine the value of the current \( i \) in the circuit. Current division should be used.
**Circuit Diagram Description:**
- The circuit diagram shows three parallel paths.
- The first path has a 2A current source in series with a 12Ω resistor.
- The second path has a 0.5A current source in series with a 3Ω resistor.
- The third path has a 1.5A current source in series with a 6Ω resistor.
**Explanation:**
This problem involves calculating the current \( i \) through one of the resistors (not labeled in the diagram provided) using the concept of current division. Current division is applicable when you have parallel branches in a circuit, allowing you to determine how current divides among the parallel branches based on their resistance values. In this setup, each path has a specified resistance and a current source.
To solve such a problem, you use the formula for current division:
\[
i_x = \frac{I_{\text{total}} \cdot R_{\text{total}}}{R_x}
\]
Where:
- \( i_x \) is the current through the resistor in question.
- \( I_{\text{total}} \) is the total current supplied to the parallel network.
- \( R_{\text{total}} \) is the total resistance of the parallel network.
- \( R_x \) is the resistance through which you want to find the current.
Since full values aren't given, you will need to apply the concept ideally utilizing the data and conditions provided in the diagram.
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