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Kirchhoff's Rules for Circuits E, = 24.0 V Use Kirchhoff's loop and junction rules to set up b d a system of 3 linear equations that could be solved for the 3 unknown currents, I1, I2, 13, in the circuit to the right. 0.10 2 R, 5.0 2 Rs 20 2 E2 = 48.0 V simplify each of your equations, express R2 12 them without units, and box them. a e 0.50 N 40 2 Do not attempt to solve. Your equations should be numerical and placed in the 20.20 2 R 78 Ω standard linear algebra system of equations form we used in lab. For example: E = 36.0 V Ez = 6.0 V r3 5.11 + 2.413 = -4.9 i 0.05 Ω h

Kirchhoff's Rules for Circuits E, = 24.0 V Use Kirchhoff's loop and junction rules to set up b d a system of 3 linear equations that could be solved for the 3 unknown currents, I1, I2, 13, in the circuit to the right. 0.10 2 R, 5.0 2 Rs 20 2 E2 = 48.0 V simplify each of your equations, express R2 12 them without units, and box them. a e 0.50 N 40 2 Do not attempt to solve. Your equations should be numerical and placed in the 20.20 2 R 78 Ω standard linear algebra system of equations form we used in lab. For example: E = 36.0 V Ez = 6.0 V r3 5.11 + 2.413 = -4.9 i 0.05 Ω h

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**Kirchhoff’s Rules for Circuits** 7. Use Kirchhoff’s loop and junction rules to set up a system of 3 linear equations that could be solved for the 3 unknown currents, \(I_1, I_2, I_3\), in the circuit to the right. **Simplify** each of your equations, express them without units, and **box** them. Do not attempt to solve. Your equations should be numerical and placed in the standard linear algebra system of equations form we used in lab. For example: \[ \boxed{5.1I_1 + 2.4I_3 = -4.9} \] **Circuit Diagram Explanation:** - The diagram consists of a circuit including four electromotive forces (\(\mathcal{E}_1 = 24.0 \, V\), \(\mathcal{E}_2 = 48.0 \, V\), \(\mathcal{E}_3 = 6.0 \, V\), \(\mathcal{E}_4 = 36.0 \, V\)). - There are resistors with the following resistances: \(R_1 = 5.0 \, \Omega\), \(R_2 = 40 \, \Omega\), \(R_3 = 78 \, \Omega\), \(R_5 = 20 \, \Omega\), and small resistances \(r_1 = 0.10 \, \Omega\), \(r_2 = 0.50 \, \Omega\), \(r_3 = 0.05 \, \Omega\), \(r_4 = 0.20 \, \Omega\). - The current directions (\(I_1, I_2, I_3\)) are marked with blue arrows, indicating the paths of currents through different branches of the circuit. - Junctions in the circuit are marked with letters (e.g., a, b, c, d, etc.). - The task is to apply Kirchhoff's laws to create a system of equations that represents the currents in the circuit.
Transcribed Image Text:**Kirchhoff’s Rules for Circuits** 7. Use Kirchhoff’s loop and junction rules to set up a system of 3 linear equations that could be solved for the 3 unknown currents, \(I_1, I_2, I_3\), in the circuit to the right. **Simplify** each of your equations, express them without units, and **box** them. Do not attempt to solve. Your equations should be numerical and placed in the standard linear algebra system of equations form we used in lab. For example: \[ \boxed{5.1I_1 + 2.4I_3 = -4.9} \] **Circuit Diagram Explanation:** - The diagram consists of a circuit including four electromotive forces (\(\mathcal{E}_1 = 24.0 \, V\), \(\mathcal{E}_2 = 48.0 \, V\), \(\mathcal{E}_3 = 6.0 \, V\), \(\mathcal{E}_4 = 36.0 \, V\)). - There are resistors with the following resistances: \(R_1 = 5.0 \, \Omega\), \(R_2 = 40 \, \Omega\), \(R_3 = 78 \, \Omega\), \(R_5 = 20 \, \Omega\), and small resistances \(r_1 = 0.10 \, \Omega\), \(r_2 = 0.50 \, \Omega\), \(r_3 = 0.05 \, \Omega\), \(r_4 = 0.20 \, \Omega\). - The current directions (\(I_1, I_2, I_3\)) are marked with blue arrows, indicating the paths of currents through different branches of the circuit. - Junctions in the circuit are marked with letters (e.g., a, b, c, d, etc.). - The task is to apply Kirchhoff's laws to create a system of equations that represents the currents in the circuit.
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