c) Now go back to the full circuit in the figure. Use Kirchoff's laws to write down one node equation, and two loop equations for loop 1 and loop 2. Keep the direction of the currents the same as in the Figure. I = Iz + I, loop ! : O: - I, Ry + I, R2 loop 2 : 0= 12V - Iz R2 - I,R, 'd) Use your answers above to calculate current is. I, = IgRy/ Ra 2 , I , = I , + I , : Ig help + Is = Is ( Rut Rx ) 0 = 12 V - I, Ry/p . R 2 - I, ( RX + Rx ) R RZ 0 = 12 V. I, 5M. I, 8. 252 0 - 361 _ I, ( 15.52 + 16 12 ) - I, = 364 - 1.16A d) [EXTRA CREDIT QUESTION (5 points)] We now modify the circuit above by addingRa = 50 13 loop 1 12 R, = 20 11 R2 = 30 loop 2 + V = 12V