Use Kirchhoff's rules to find the equations that solve for the currents in the following circuit. You should have 5 separate equations but you do not need to solve them algebraically. I Answer: R5 80 Q2 R6 20 Ω R1 60 Ω BAT1 12 V BAT4 9 V R3 30 22 R2 20 22 R4 60 Ω Write your 5 equations in the below boxes BAT3 1.5 V Thanogmco

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**Educational Worksheet: Applying Kirchhoff's Rules**

**Objective:** Use Kirchhoff's rules to derive equations for the currents in the given electrical circuit. You are required to establish 5 separate equations, however, solving them algebraically is not necessary.

**Diagram Analysis:**
The circuit diagram consists of the following components:

- **Batteries:**
  - BAT1: 12 V
  - BAT3: 1.5 V
  - BAT4: 9 V

- **Resistors:**
  - R1: 60 Ω
  - R2: 20 Ω
  - R3: 30 Ω
  - R4: 60 Ω
  - R5: 80 Ω
  - R6: 20 Ω

The circuit is composed of multiple loops and branches that require analysis using Kirchhoff's Voltage and Current Laws to establish the necessary equations.

**Procedure:**

1. **Identify Loops and Nodes:**
   - Determine all the loops in the circuit.
   - Identify nodes where currents converge or diverge.

2. **Apply Kirchhoff's Voltage Law (KVL):**
   - For each loop, the sum of the electromotive forces (emf) and the potential differences (voltage drops) across resistors must be zero.
   - Establish equations based on the voltage drops and rises around the loops.

3. **Apply Kirchhoff's Current Law (KCL):**
   - At each node, the sum of currents entering the node is equal to the sum of currents leaving the node.
   - Write equations based on the current conservation at junctions.

**Answer:**

*Write your 5 equations in the below boxes:*

1. _______________________________________________________________

2. _______________________________________________________________

3. _______________________________________________________________

4. _______________________________________________________________

5. _______________________________________________________________

**Instructions:**
Fill in the boxes with the equations derived from applying Kirchhoff's laws to the circuit. Remember to consider the directionality of currents and voltage drops. 

This exercise strengthens the understanding of circuit analysis and the application of fundamental electrical engineering principles.
Transcribed Image Text:**Educational Worksheet: Applying Kirchhoff's Rules** **Objective:** Use Kirchhoff's rules to derive equations for the currents in the given electrical circuit. You are required to establish 5 separate equations, however, solving them algebraically is not necessary. **Diagram Analysis:** The circuit diagram consists of the following components: - **Batteries:** - BAT1: 12 V - BAT3: 1.5 V - BAT4: 9 V - **Resistors:** - R1: 60 Ω - R2: 20 Ω - R3: 30 Ω - R4: 60 Ω - R5: 80 Ω - R6: 20 Ω The circuit is composed of multiple loops and branches that require analysis using Kirchhoff's Voltage and Current Laws to establish the necessary equations. **Procedure:** 1. **Identify Loops and Nodes:** - Determine all the loops in the circuit. - Identify nodes where currents converge or diverge. 2. **Apply Kirchhoff's Voltage Law (KVL):** - For each loop, the sum of the electromotive forces (emf) and the potential differences (voltage drops) across resistors must be zero. - Establish equations based on the voltage drops and rises around the loops. 3. **Apply Kirchhoff's Current Law (KCL):** - At each node, the sum of currents entering the node is equal to the sum of currents leaving the node. - Write equations based on the current conservation at junctions. **Answer:** *Write your 5 equations in the below boxes:* 1. _______________________________________________________________ 2. _______________________________________________________________ 3. _______________________________________________________________ 4. _______________________________________________________________ 5. _______________________________________________________________ **Instructions:** Fill in the boxes with the equations derived from applying Kirchhoff's laws to the circuit. Remember to consider the directionality of currents and voltage drops. This exercise strengthens the understanding of circuit analysis and the application of fundamental electrical engineering principles.
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