Q 1. Kirchhoff's laws show that R 2R I – I2 – I3 =0 ɛ – RI1 – RI2 =0 (1) (2) | R dI3 =0 dt ɛ – RI – 2RI3 (3) - This can be simplified into a single equation for I3 by inserting eq. (1) for I2 in eq. (2). We get E – RI1 – R(I1 – I3) = € – 2RI1 + RI3 = 0 and therefore I1 yields an inhomogeneous first order ODE for I3 I3 Inserting this in eq. (3) 2R' dI3 I3 – L dt 5R 2 0 = Observe that this has the same structure as compared to the equation we had in lecture for the dI rising current through an inductor with resistor: V – RI – L 0. - - dt By equating the coefficients from both equations find the current as a function of time trough the inductor if the switch is closed at t = 0 in the the figure. Also find the current trough the switch as a function of time. ll

Q 1. Kirchhoff's laws show that R 2R I – I2 – I3 =0 ɛ – RI1 – RI2 =0 (1) (2) | R dI3 =0 dt ɛ – RI – 2RI3 (3) - This can be simplified into a single equation for I3 by inserting eq. (1) for I2 in eq. (2). We get E – RI1 – R(I1 – I3) = € – 2RI1 + RI3 = 0 and therefore I1 yields an inhomogeneous first order ODE for I3 I3 Inserting this in eq. (3) 2R' dI3 I3 – L dt 5R 2 0 = Observe that this has the same structure as compared to the equation we had in lecture for the dI rising current through an inductor with resistor: V – RI – L 0. - - dt By equating the coefficients from both equations find the current as a function of time trough the inductor if the switch is closed at t = 0 in the the figure. Also find the current trough the switch as a function of time. ll