Please answer all the question using mathematics thanks Con

Please answer all the question using mathematics thanks :)

Consider the circuit pictured in figure below. Let I_1 (t), I_2(t) represent the current flow across the inductors L_1(t), L_2(t) respectively. Show that the circuit is modeled by the system: {L_1 I_1 = -R_1I_1 - R_2I_2 +E L_2I_2 = -R_1 I_1 - (R_1 + R_2)I_2 + E Solve the system if: E = e^t/2, L_1 = L_2 = 0.5, R_1 = R_2 = 1

Solution

1. Clearly E=L1I1+R1I1+R2I2 and thus

L1I1= -R1I1-R2I2+E

similarly, E= R1I1+(R1+R2)IT+L2I2 which gives us

L2I2= -R1I1-(R1+R2)IT +E

2. Putting the values of E,L1I1,L2I2,R1,RE in bother the above equation we get

I1=3I2