(Solved): The equivalent model of a permanent magnet DC motor is shown in Figure 2.1. All the symbols in the ...

The equivalent model of a permanent magnet DC motor is shown in Figure 2.1. All the symbols in the figure represent standard quantities and parameters related to the equivalent model. Assume that the viscous friction of the system is negligible. Figure 2.1 Equivalent model of a permanent magnet DC motor a. State all governing equations corresponding to the operation of the DC motor with the following parameter values and show the necessary derivations. $${\mathrm{r}}_{\mathrm{a}}=0.5?,{\mathrm{k}}_{\mathrm{a}}=0.05{\mathrm{NmA}}^{?1},{\mathrm{L}}_{\mathrm{a}}=0.02\mathrm{H}\text{, and }\mathrm{J}=0.0004{\mathrm{kgm}}^2$$ d. Calculate the stall current and stall torque if $$u_a$$ was set to $$18\mathrm{V}$$. e. Calculate the no-load steady-state speed and current of the motor when $${\mathrm{u}}_{\mathrm{a}}=18\mathrm{V}$$. f. Find the steady-state speed and current if the load torque $$T_L$$ varies with $${?}_{\mathrm{r}}$$ as follows at $${\mathrm{u}}_{\mathrm{a}}=18\mathrm{V}$$. $$T_L=0.05+2.5\times 10^{?6}{?}_r^2\mathrm{Nm}$$