Circuit with 2 Batteries and 6 Resistors

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SUMMARY

The discussion revolves around a circuit analysis problem involving two batteries (V1 = 18 V and V2 = 12 V) and six resistors with specified values: R1 = R5 = 73 Ω, R2 = R6 = 121 Ω, R3 = 62 Ω, and R4 = 92 Ω. The equations derived from Kirchhoff's laws are used to solve for the voltages and currents in the circuit, specifically V4, I1, I2, and I3. The equations include relationships such as I3R3 + I1R1 - ΔV1 = 0 and I6R6 - ΔV2 + I2R2 + I1R1 = 0, which are essential for determining the unknowns in the circuit.

PREREQUISITES
  • Understanding of Kirchhoff's Voltage and Current Laws
  • Familiarity with Ohm's Law (V=IR)
  • Basic circuit analysis techniques
  • Ability to solve simultaneous equations
NEXT STEPS
  • Study advanced circuit analysis techniques using mesh and nodal analysis
  • Learn about Thevenin's and Norton's theorems for circuit simplification
  • Explore the impact of varying resistor values on circuit behavior
  • Investigate the use of simulation software like LTspice for circuit analysis
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Homework Statement


[/B]
A circuit is constructed with six resistors and two batteries as shown. The battery voltages are V1 = 18 V and V2 = 12 V. The positive terminals are indicated with a + sign, The values for the resistors are: R1 = R5 = 73 Ω, R2 = R6 = 121 Ω R3 = 62 Ω, and R4 = 92 Ω. The positive directions for the currents I1, I2 and I3 are indicated by the directions of the arrows. What is V4, I1, I2, and I3?

Homework Equations



V=IR

The Attempt at a Solution


-I3R3+I1R1-ΔV1=0
+I6R6-ΔV2+I2R2+I1R1=0
-I1R1-I2R2-I5R5-I4R4-I6R6=0
-ΔV1-I3R3-I2R2+ΔV2-I6R6=0
-ΔV2-I5R5-I4R4=0
-I4R4-I6R6-ΔV1-I3R3-I2R2-I5R5=0

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