Circuit Analysis: Current Through R3

Circuit Analysis Problem

Given Values

• Resistances:
  • R₁ = 420 Ω
  • R₂ = 380 Ω
  • R₃ = 780 Ω
  • R₄ = 300 Ω
  • R₅ = 180 Ω
• Voltage Source:
  • E₅ = 3.6 V

Objective

• Determine the current flow through resistor R₃.

Analysis Approach

1. **Identify Configuration: **

   • The resistors can be in series and/or parallel. Determine how they are connected in the circuit to analyze the flow of current.

2. Calculate Equivalent Resistance:

   • If resistors are in series, add their resistances:
     $R<em>{eq} = R</em>1 + R<em>2 + … + R</em>n$
   • If resistors are in parallel, use:
     $\frac{1}{R<em>{eq}} = \frac{1}{R</em>1} + \frac{1}{R<em>2} + … + \frac{1}{R</em>n}$

3. Apply Ohm’s Law:

   • Once the equivalent resistance is calculated, use Ohm's Law to find the total current:
     $I = \frac{V}{R_{eq}}$

4. Current Division:

   • If R₃ is in parallel with other resistors, use current division to find the current specifically through R₃:
     $I<em>{R3} = I</em>{total} imes \frac{R<em>{total}}{R</em>3}$

Given Options for Current Flow Through R₃

• Answer Choices:
  • a. 0.79 A
  • b. 1.1 A
  • c. 9.5 mA
  • d. 12.3 mA
  • e. 20 mA
  • f. 32.3 mA

Conclusion

• Based on calculated total current and its distribution in the circuit, select the correct numerical value from the options provided after performing necessary calculations for the current through R₃.