Found 1006 Articles for Electronics & Electrical

The DC motors can be stopped using one of the following methods −Mechanical (Friction) BreakingElectric BreakingIn mechanical breaking, the motor is stopped due to friction between the moving parts of the motor and the break shoe. The mechanical breaking has several disadvantages as non-smooth stop, wear and tear of moving parts, breaking power wasted as heat and greater stopping time etc.In electric breaking, the kinetic energy of moving parts of the motor is converted into electrical energy which is either dissipated in a resistance or returned to the supply source. Types of Electric BreakingThere are three types of electric breaking methods ... Read More

Efficiency of DC GeneratorThe efficiency of a DC generator is defined as the ratio of mechanical input power to the output electrical power.$$\mathrm{Efficiency, \:\eta\:=\frac{Electrical\:Power\:Output(P_{o})}{ Mechanical\:Power\:Input(P_{i})}}$$ExplanationConsider the power flow diagram of a DC generator (see the figure), here the power is represented in three stages asBy referring the power flow diagram, $$\mathrm{Iron\:and\:Friction\:Losses\:=\:𝐴\:−\:𝐵}$$$$\mathrm{Copper\:Losses\:=\:𝐵\:−\:𝐶}$$Therefore, the efficiency of a DC generator can also be defined for the three stages as followsMechanical Efficiency  −$$\mathrm{\eta_{mech}\:=\frac{B}{A}=\:\frac{Power\:Developed\:in\:Armature\:(E_{g}I_{a})}{Mechanical\:Power\:Input\:(P_{i})}}$$Electrical Efficiency −$$\mathrm{\eta_{elect}\:=\frac{C}{B}=\:\frac{Electric\:Power\:Output\: (VI_{L})}{Power\:Developed\:in\:Armature\:(E_{g}I_{a})}}$$Commercial Efficiency − (always consider this unless stated otherwise)$$\mathrm{\eta\:=\frac{C}{A}=\:\frac{Power\:Output\:(P_{o})}{Power\:input\:(P_{i})}}$$Condition for Maximum EfficiencyThe efficiency of a DC generator is not constant but changes with the change in load.Let, for a ... Read More

Efficiency of a DC MotorThe efficiency of a DC motor is defined as the ratio of output power to the input power.Mathematically, $$\mathrm{Efficiency, \eta \:=\:\frac{Power\:Output}{Power\:Intput}\times 100 \%\:=\:\frac{P_{out}}{P_{in}}\times100\%\:...(1)}$$Since, $$\mathrm{Power\:input, \:P_{in} = Power\:Output(P_{out}) + Losses}$$Therefore, $$\mathrm{Efficiency, \eta \:=\:\frac{P_{out}}{P_{out}\:+\:losses}\times100\%\:....(2)}$$Condition for Maximum Efficiency of DC MotorThe efficiency of a DC motor is not constant but varies with the load. Consider a shunt motor (as shown in the figure) drawing an armature current of Ia amperes and the back emf is Eb.The mechanical power developed by the motor is (neglecting the mechanical losses), $$\mathrm{P_{m}=P_{out}=E_{b}I_{a}}$$The input power to the motor is, $$\mathrm{P_{in}=P_{out}\:+\:variable\:losses\:+\:constant\:losses}$$$$\mathrm{Efficiency, \eta\:=\:\frac{P_{out}}{P_{in}}\:=\:\frac{E_{b}I_{a}}{P_{out}\: +\:variable\:losses\:+\:constant\:losses}}$$$$\mathrm{⇒\eta\:=\:\frac{E_{b}I_{a}}{E_{b}I_{a}\:+\:I_a^2R_{a}\:+\:W_{c}}}$$$$\mathrm{⇒\eta\:=\:\frac{1}{1+(\frac{I_{a}R_{a}}{E_{b}})+\frac{W_{c}}{E_{b}I_{a}}}\:....(3)}$$The efficiency of ... Read More

An autotransformer is a one winding transformer in which a part of the winding is common to both primary and secondary windings.An autotransformer has a single continuous winding with a tap point between the primary and secondary windings. The tap point can be adjusted to obtain the desired output voltage, hence this is an obvious advantage of the autotransformer. The main disadvantage of an autotransformer is that the secondary winding is not electrically isolated from the primary.Theory of AutotransformerCase 1 – Autotransformer on No-LoadThe connection diagram of an unloaded autotransformer (step-down and step-up) is shown in the figure. In this, ... Read More

A current transformer (C.T.) is an instrument transformer which is used for the protection and measurement purposes in a power system. The C.T. is primarily used to measure high alternating currents in a power system.Construction of Current TransformerThe magnetic core of the current transformers is made up of thin laminations of silicon steel. The primary winding of a CT has a single turn (also called bar primary) and carries full-load current whereas the secondary winding has large number of turns. Therefore, the current transformer is a voltage step-up and current step-down transformer (see the figure).The primary winding of the current ... Read More

A transformer needs less magnetic material if it is operated at a higher core flux density. Thus, from the economic point of view, a transformer is designed to operate in the saturation region of the magnetic core.When a sinusoidal voltage is applied to the primary winding of the transformer, then the mutual flux set-up in the core is assumed to be sinusoidal and the no-load or exciting current (I0) will be non-sinusoidal due to hysteresis loop. It contains fundament and all odd harmonics.Consider the hysteresis loop of the core of the given transformer as shown in the figure below. Since, ... Read More

There is a sudden inrush of the primary current, when the transformer is initially energized and the maximum value of the magnetic flux is more than twice the normal value of the flux. Hence, due to the very high peak of the magnetising current, the core is driven far into saturation.Let a sinusoidal voltage is applied to the primary winding of a transformer is$$\mathrm{𝑣_{1} = u_{1𝑚}\:sin(\omega 𝑡 + 𝜃) … (1)}$$And the secondary winding of the transformer is kept open circuited. Here, θ is the angle of the voltage at t = 0.Now, if the core losses and the primary ... Read More

The three-phase transformer vector groups are divided into four main groups depending on the phase difference between the corresponding line voltages on the high-voltage and lowvoltage sides. The angle by which the line voltage on the low-voltage side lags behind the line voltage on the high-voltage side is called as the phase difference and it is measured in the units of 30° in the clockwise direction.The four transformer vector groups are −Group 1 – No Phase Displacement, i.e., 0° Phase DisplacementGroup 2 – Phase Displacement of 180°Group 3 – Phase Displacement of -30°Group 4 – Phase Displacement of +30°Now, instead ... Read More

A three phase transformer is required to step-up or step-down the three phase voltages in a power system. The 3-phase transformers can be constructed in one of the following ways −Three separate 1-phase transformers can be connected for the 3-phase operation. Such an arrangement is known as 3-phase bank of transformers.A single three phase transformer can be constructed in which the cores and windings for all the three phases are combined in a single structure.Construction of a Three Phase TransformerThe figure shows the core type and the shell type construction of the three-phase transformer. The 3-phase transformer consists of a ... Read More

The circuit arrangement of the transformers for three-to-twelve phase transformation is shown in the figure.Here, two banks of three 1-phase transformers or two 3-phase transformers are required. In this connection, the secondary windings are arranged in the form of pair of double-star connections. The primary windings of one set of transformers or of one of 3-phase transformers being connected in star while the primary windings of the other being connected in delta. Hence, the arrangement can be named as star-delta / double-star connection for transforming 3-phase to 12-phase. The phasor diagrams of both sets of transformers are shown in the ... Read More