### Calculate the no-load current and power factor

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##### Reference no: EM13857523

Transformer Design

A single phase transformer core, for use in a 50Hz electrical network, has the following magnetic characteristic

The core has a cross-sectional area of 175cm2, the mean magnetic path length is 160cm and the density of the core material is 7.5gm/cm3.

(a) If a no-load voltage ratio of 6600/231 is required, choose a suitable number of primary and secondary turns so that the maximum flux density in the core does not exceed 1.2 Tesla. [NB: E = 4.44fN2f]

(b) Using these turns, calculate the no-load current and power factor at normal operating voltage. Note that you should allow an additional 50 Ampere-Turns to compensate the increased reluctance of the magnetic path resulting from gaps between "E-" and "I-sections" of the core laminations.

Although your answer will be based on mathematical calculation, your results will require some interpretation and the application of engineering judgement before you reach a final answer. You should provide suitable written justification of your design decisions.

DC Motor Model

A separately excited DC motor has a load consisting of an inertia J kg m2 with viscous damping B Nm per rad/s. Develop electromechanical models (transfer functions) for the motor to relate how the rotor shaft angle can be controlled using:

(a) Field voltage Vf control, i.e. develop the transfer function ?(s)/Vf(s)

(b) Armature voltage Va control, i.e. develop the transfer function ?(s)/Va(s)

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