Question

Find the currents , 2 and l in the circuit shown in the figure where 16 V Conceptualize: We cannot simplify the circuit by the rules associated with combining resistances in series and in parallel. (If the 10.0 V battery was not present, we could reduce the remaining circuit with series and parallel combinations.) Categorize: Because the circuit is not a simple series and parallel combination of resistances, this problem is one in which we must use Kirchhoff's rules. Analyze: We arbitrarily choose the directions of the currents as labeled in the figure. Apply Kirchhott's junction nule to junction unknowns: ly, and J:-There are three loops in the circuit: ada,ch, and adda determine the unknown currents. (The information) Ler's in the clockwise direction and bokk Solve Equation (3) for , and substitute into Equation (2) Multiply each term in Equation (3) by 4 4)100 V-(8.0M-(.0,- and each term in Equation (4) by3 Add Equation (6) to Equation ()to eiminate』·and find Use this value of i in Equation (3) s find -260 V ◆ (6.012), + 13.456 V·0 Use Equation (1) to find ら"ri +1,-(2.001 A1+(-3.364A) Finalize: Because our values for /2 and I3 are negative, the directions of these currents are opposite those indicated in the figure. The numerical values for the currents are correct. Despite the incorrect direction, we must continue to use these negative values in subsequent calculations because our equations were established with our original choice of direction.