The inductances of two mutually coupled coils are: l11 = a = l22 and l12 = l21 = b cos θ , where a and b are constants. the windings are both connected to two source currents i1 and i2. (a) derive an expression for the electromagnetic torque as a function of θ, i1, and i2. (b) find the developed electromagnetic torque for i1 = i0 and i2 = 0. (c) find the developed electromagnetic torque for i1 = i2 = i0. (d) find the developed electromagnetic torque for i1 = im sin ωt and i2 = i0. (e) (i) find the developed electromagnetic torque for i1 = i2 = im sin ωt. (ii) find the value(s) of speed ωm at which the machine will develop an average torque if θ = ωmt - δ. (iii)find the maximum torque and power (mechanical) that could be developed by the machine at each speed. (f) (i) find the developed electromagnetic torque for i1 = im sin ωt and i2 = im cos ωt.. (ii) find the value(s) of speed ωm at which the machine will develop an average torque if θ = ωmt - δ. (iii)find the maximum torque and power (mechanical) that could be developed by the machine at each speed. (b) find the developed electromagnetic torque for i1 = i0 and coil 2 is short-circuited.