Write Kirchhoff\'s equations for the circuit shown in Fig. 1 (at first in terms

Question

Write Kirchhoff's equations for the circuit shown in Fig. 1 (at first in terms of assigned currents I_1,I_2,I_3, resistors R_1,R_2,R_3, and voltages V_1,V_2,V_3). Then plug in in these equations the following values: R_1-6.0 Ohm, R_2 = 9.0 Ohm, R_3 = 8.0 Ohm; V_1 = 14.0 V, V_3 = 10.0 V. Present the equations in the form with numerical coefficients A and constant terms B_J (which is convenient for application of Cramer's (determinant) method). Then solve this system of three algebraic equations and verify your solution.

Explanation / Answer

KVL in loop 1:

V3 - I3R3 - I1R1 - V1 = 0

R1 I1 + R3 I3 = V3 - V1

KVL in loop 2:

-I2R2 + I3R3 - V3 - V2 = 0

-R2I2 + R3 I3 = V2 + v3

KCL:

I2 + I3 = I1

I2 - I2 - I3 = 0

So equation are ( Putting values) :

6I1 + 0 I2 + 8I3 = 2

0 I1 - 9I2 + 8I3 = 24

I1 - I2 - I3 = 0

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