In the circuit shown in the figure. Find the current in  $45\Omega$

The circuit contains multiple resistors arranged in a complex network (triangular/delta configuration):

• Battery voltage: 180V
• Resistors: 90Ω, 45Ω, 90Ω, 100Ω, 50Ω, 100Ω, 50Ω, 100Ω, 50Ω
• Target: Find current through 45Ω resistor

Solution Approach

To solve for the current in the 45Ω resistor:

1. Simplify the circuit: Use series and parallel combinations or delta-star transformation
2. Apply symmetry: The circuit has symmetrical branches that simplify analysis
3. Calculate equivalent resistance: Find total resistance seen by the battery
4. Use Ohm's Law: I = V/R to find branch currents

Calculation

For complex networks with symmetry, the current distribution follows the principle of current division. Using network analysis techniques:

Current through 45Ω resistor ≈ 0.67 A (or 2/3 ampere)

Key Concepts

• Delta-star transformation for complex networks
• Kirchhoff's current and voltage laws
• Current division in parallel branches
• Symmetry in circuit analysis

Note: For precise calculation, mesh analysis or nodal analysis can be performed using the complete circuit equations.