Ig エ」 In the following diagram, use Kirchhoff's rules to solve In 12V 8V Iレ current passing through3 ohm resistor, Iz = ? I, 4L I,

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**Kirchhoff's Rules - Circuit Analysis**

In the following diagram, use Kirchhoff's rules to solve for the current passing through the 3 ohm resistor, \( I_3 = ? \)

**Circuit Diagram Explanation:**

The diagram depicts a circuit consisting of multiple resistors and voltage sources arranged in two loops. The key components include:

- **Resistors:** 
  - \( 5 \, \Omega \)
  - \( 6 \, \Omega \)
  - \( 3 \, \Omega \)
  - \( 4 \, \Omega \)

- **Voltage Sources:**
  - \( 8 \, \text{V} \)
  - \( 12 \, \text{V} \)

- **Current Paths:**
  - \( I_1 \) passes through the \( 5 \, \Omega \) resistor.
  - \( I_2 \) flows through the \( 6 \, \Omega \) resistor and part of the loop with the \( 8 \, \text{V} \) battery.
  - \( I_3 \) traverses the \( 3 \, \Omega \) resistor along with part of the loop containing the \( 12 \, \text{V} \) battery and the \( 4 \, \Omega \) resistor.
  
The objective is to find the current \( I_3 \) passing through the \( 3 \, \Omega \) resistor using Kirchhoff's rules. 

Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) should be applied around the loops and junctions to determine the currents.
Transcribed Image Text:**Kirchhoff's Rules - Circuit Analysis** In the following diagram, use Kirchhoff's rules to solve for the current passing through the 3 ohm resistor, \( I_3 = ? \) **Circuit Diagram Explanation:** The diagram depicts a circuit consisting of multiple resistors and voltage sources arranged in two loops. The key components include: - **Resistors:** - \( 5 \, \Omega \) - \( 6 \, \Omega \) - \( 3 \, \Omega \) - \( 4 \, \Omega \) - **Voltage Sources:** - \( 8 \, \text{V} \) - \( 12 \, \text{V} \) - **Current Paths:** - \( I_1 \) passes through the \( 5 \, \Omega \) resistor. - \( I_2 \) flows through the \( 6 \, \Omega \) resistor and part of the loop with the \( 8 \, \text{V} \) battery. - \( I_3 \) traverses the \( 3 \, \Omega \) resistor along with part of the loop containing the \( 12 \, \text{V} \) battery and the \( 4 \, \Omega \) resistor. The objective is to find the current \( I_3 \) passing through the \( 3 \, \Omega \) resistor using Kirchhoff's rules. Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current Law (KCL) should be applied around the loops and junctions to determine the currents.
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