Ɛz= 18 V 0.5 Q R. 2.5Q- I, R, a R 1.5 2 0.5 N E2 = 45 V What equation do you get when you apply the loop rule to the loop abcdefgha, in terms of the variables in the figure? 0 = If the current through the top branch is I, = 0.57 A, what is the current through the bottom, I3, in amps?

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The image shows an electrical circuit with the following components and notations:

### Circuit Components:
- **Voltage Sources:**
  - \( \mathcal{E}_1 = 18 \, \text{V} \) located between points b and a.
  - \( \mathcal{E}_2 = 45 \, \text{V} \) located between points h and g.
  
- **Resistors:**
  - \( R_1 = 0.5 \, \Omega \) between points d and e.
  - \( R_2 = 2.5 \, \Omega \) between points b and a (parallel with \( \mathcal{E}_1 \)).
  - \( R_3 = 1.5 \, \Omega \) between points e and f.
  
- **Current Directions:**
  - \( I_1 \) flows from c to d.
  - \( I_2 \) flows upward from a to b.
  - \( I_3 \) flows downward from h to a in the bottom branch.

### Questions and Equations:
1. **Application of Loop Rule:**
   - What equation do you get when you apply the loop rule to the loop abcdefgha, in terms of the variables in the figure?

     \[ 0 = \]

2. **Current Calculation:**
   - If the current through the top branch is \( I_2 = 0.57 \, \text{A} \), what is the current through the bottom, \( I_3 \), in amps?

     \[ I_3 = \]

This circuit is used to solve for unknown currents using the loop rule (also known as Kirchhoff's voltage law), which states that the sum of the electromotive forces and potential differences (voltage) in any closed loop of a circuit is equal to zero.
Transcribed Image Text:The image shows an electrical circuit with the following components and notations: ### Circuit Components: - **Voltage Sources:** - \( \mathcal{E}_1 = 18 \, \text{V} \) located between points b and a. - \( \mathcal{E}_2 = 45 \, \text{V} \) located between points h and g. - **Resistors:** - \( R_1 = 0.5 \, \Omega \) between points d and e. - \( R_2 = 2.5 \, \Omega \) between points b and a (parallel with \( \mathcal{E}_1 \)). - \( R_3 = 1.5 \, \Omega \) between points e and f. - **Current Directions:** - \( I_1 \) flows from c to d. - \( I_2 \) flows upward from a to b. - \( I_3 \) flows downward from h to a in the bottom branch. ### Questions and Equations: 1. **Application of Loop Rule:** - What equation do you get when you apply the loop rule to the loop abcdefgha, in terms of the variables in the figure? \[ 0 = \] 2. **Current Calculation:** - If the current through the top branch is \( I_2 = 0.57 \, \text{A} \), what is the current through the bottom, \( I_3 \), in amps? \[ I_3 = \] This circuit is used to solve for unknown currents using the loop rule (also known as Kirchhoff's voltage law), which states that the sum of the electromotive forces and potential differences (voltage) in any closed loop of a circuit is equal to zero.
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