Repeat Example 7.7 with the resistor R₁ changed to 100. ohms and all other values unchanged.

Example 7.7

Find the current through and voltage across the 40. ohm resistor, R₃, in the following circuit.

 

Need: I₃ = ____ A and V₃ = ____ V.

Know: Kirchhoff’s current and voltage laws, Equations (7.3) and (7.5).

How: This circuit has four nodes (A, B, C, and D) and two independent loops. Write the current law equations for the two nodes and the voltage law equations for the two loops. Then solve the resulting set of algebraic equations for the currents.

Using Kirchhoff’s current law, for node A the equation is I₁ + I₂ = I3

Using Kirchhoff’s voltage law around loops 1 and 2, the equations are:

Since I₃ is the sum of I₁ + I₂ we can substitute this into the loop equations and rewrite them as:

R2 R1 10.ohm A 12 D 20.ohm 20. v 10. v 2 R3 40.ohm V2 13