Figure illustrates the V-I charactefistics of a PN-junction diode. The charactefistics curve contains three distinct regions as,

1. Forward bias region
2. Reverse bias region
3. Breakdown region.

Forward Bias Region: On forward biasing, P side of the PN-junction is connected to the positive of the voltage supply and N side of the PN-junction is connected to the negative of the voltage supply. Simply, forward bias region is the characteristics of the diode for V > 0. From figure it can be seen that (in the FB region) initially, the diode current is very small because the barrier potential prevents the flow of current through it. If the applied voltage exceeds the barrier potential, then for a small increase in the voltage produces a shall) increase in the current. The voltage at which the current starts to increase rapidly is called cut-in or knee voltage of the diode. It is denoted as V_γ.

For silicon diode V_γ = 0.7 V and Germanium diode V_γ = 0.3V.

Reverse Bias Region: On reverse biasing, P side of the PN-junction is connected to the negative terminal of the voltage supply and N side of the PN-junction is connected to the positive terminal of the voltage supply. Simply, reverse bias region is the characteristics of the diode for V < 0. From figure it can be seen that (in RB region) the diode current is very small, almost equal to zero for all values of voltage less than the break down voltage V_Z. This is because in reverse bias the width of the potential barrier increases. As a consequence, the junction resistance becomes very high and practically no current flows through the circuit.

Breakdown Region: The diode enters the breakdown region when the magnitude of the reverse voltage exceeds a threshold value of that particular diode called the breakdown, voltage. In this region for very small variation in voltage the current increases rapidly as shown in figure. PN Diode should not be operated for V_R > V_BD because the diode will be damaged.

VI Characteristics of Ideal Diode

The deviation of V-I characteristics of pn junction diode from its ideal characteristics is illustrated below.

Figure 2.

The ideal and practical characteristics of p-n junction diode is shown in figure 2 (a) and (b) respectively.

1. When diode is forward biased.

(i) For ideal p-n diode, the forward resistance is zero. As a result, the diode acts as short circuit i.e., V = 0 and is remain unchanged for any value of ‘I’.

(ii) The practical p-n diode offers small forward resistance (i.e., static and dynamic resistance). Hence as voltage increases beyond barrier potential current also increases rapidly as shown in figure (b).

2. When diode is reverse biased.

(i) The ideal p-n diode offers infinite resistance. In this case the diode acts as open circuit i.e., current flowing through the diode is zero and the reverse voltage becomes infinite. An ideal diode does not undergo any breakdown, since the current is zero for any value of reverse voltage.

(ii) In a practical p-n diode, for an applied reverse voltage small amount of current flows due to minority charge carriers in both the regions. When the voltage increases above breakdown voltage (V_BD). The maximum reverse saturation current flows in diode. As a consequence it gets destroyed.

Note: PN Junction diode should be operated for V_R < V_BD.

The post VI Characteristics of PN Junction Diode – Explanation & Diagram appeared first on ElectricalWorkbook.

An electric current is classified into following two basic types :

1. Direct current,
2. Alternating current.

Direct Current (D.C.) :

The direct current is that current which flows continuously in one direction and has constant magnitude with respect to time. Fig. 1.1 (a) shows the graph for such a current against time.

Alternating Current (A.C.) :

Each cycle consists of two half cycles. During one of these half cycles, the current flows in one direction around the circuit and during the other in opposite direction (Fig. 1.1 b). While flowing in one particular direction, the magnitude of the current also changes in some regular manner with time.

Comparison of Alternating Current and Direct Current

Table given below gives the broad comparison between alternating current and direct current.

Applications of Direct and Alternating Currents

In the early days, small installations supplying power mainly for lighting homes and factories were utilizing direct currents. The subsequent developments led to the extensive use of alternating currents. Now-a-days, electrical energy is almost exclusively generated, transmitted, distributed and ultimately utilized in the form of alternating current only.

Some important applications of direct and alternating currents are listed below :

Applications of Direct Currents: Traction (railways), electrolytic and other electro- chemical processes, arc lamps (used for search lights and cinema projectors), telephone and telegraph systems, charging storage batteries, modern protection systems, etc.

Applications of Alternating Currents: A.C. motors, transformers, lamps, fans, majority of domestic appliances such as TVs, refrigerators, washing machines, boilers, geysers, mixers, air conditioners and innumerable other applications.

Advantages of AC Over DC

Use of alternating current offers the following principal advantages over direct current :

1. Since it is possible to build up high-voltage, high-speed a.c. generators with very large capacities, their construction and operating costs per kilowatt are low. This is not possible in case of d.c. generators.
2. The a.c. voltage can be raised or lowered very easily with the help of a simple static device known as transformer. Raising and lowering of d.c. voltage is not so easy and economical.
3. Due to adoption of high voltages, a.c. transmission is always efficient and economical. This is because higher the voltage, lesser is the current flowing through the transmission line conductors for the given power. Consequently, the weight of conductor material and power loss in the line itself are reduced.
4. A.C. motors are simple in construction, cheaper and more efficient than d.c. motors and require less maintenance.
5. A.C. can be easily converted to d.c. whenever required for some specific applications.

The post Difference Between AC and DC appeared first on ElectricalWorkbook.

Figure (1): RLC Series Circuit.

An RLC series circuit consisting of a resistor ‘R’ Ohm (Ω) in series with an inductance of ‘L’ Henrys and capacitance of ‘ C’ Farads connected to an A.C supply as shown in figure (1).

Applying Kirchhoff’s voltage law to the above circuit,

\[V={{V}_{R}}+{{V}_{L}}+{{V}_{C}}=IR+I{{X}_{L}}+I{{X}_{C}}\]

Where,

V = Source voltage

V_R = Voltage drop across resistor = I_R

V_L = Voltage drop across inductor = IX_L

V_C = Voltage drop across capacitor = IX_C

Figure (2): RLC Series Circuit Phasor Diagram when V_L > V_C.

The phasor diagram is drawn taking the current as the reference phasor as shown in figure (2).

From the phasors diagram

\[O{{E}^{2}}=O{{A}^{2}}+O{{D}^{2}}\]

\[{{V}^{2}}=V_{R}^{2}+{{\left( {{V}_{L}}-{{V}_{C}} \right)}^{2}}\]

\[V=\sqrt{V_{R}^{2}+{{\left( {{V}_{L}}-{{V}_{C}} \right)}^{2}}}\]

\[V=\sqrt{{{\left( IR \right)}^{2}}+{{\left( I{{X}_{L}}-I{{X}_{C}} \right)}^{2}}}\]

\[V=I\sqrt{{{R}^{2}}+{{\left( {{X}_{L}}-{{X}_{C}} \right)}^{2}}}\]

\[V=IZ\]

Where,

\[Z=\sqrt{{{R}^{2}}+{{X}^{2}}}\Omega \]

= Impedance of the circuit.

From the phasor diagram here, three cases arise.

1. X_L > X_C i.e., X_L – X_C is positive
2. X_C > X_L i.e., X_L – X_C is negative
3. X_L = X_C i.e., X_L – X_C is zero.

Case (i): X_L > X_C

From the phasor diagram shown in figure (2), the net reactance is inductive. Therefore, for the condition X_L > X_C the circuit behaves like an inductive circuit. The current lags behind the voltage by 90º.

Net reactance,

\[X={{X}_{L}}-{{X}_{C}}\]

Impedance,

\[Z=\sqrt{{{R}^{2}}+{{X}^{2}}}\Omega \]

The phase difference between voltage and current,

\[\phi ={{\tan }^{-1}}\left( \frac{X}{R} \right)={{\tan }^{-1}}\left( \frac{{{X}_{L}}-{{X}_{C}}}{R} \right)\]

The power taken by the circuit,

\[P=VI\cos \phi \text{    watts}\]

Since pure inductance and capacitance do not consume power, power factor of the given circuit is $\cos \phi$ lagging.

Case (ii): X_C > X_L

Figure (3): RLC Series Circuit Phasor Diagram when X_C > X_L.

From the phasor diagram shown in figure (3), the net reactance is capacitive. Therefore, for the condition X_C > X_L the circuit behaves like a capacitive circuit. The current leads voltage by 90º.

Net reactance,

\[X={{X}_{L}}-{{X}_{C}}\]

Impedance,

\[Z=\sqrt{{{R}^{2}}+{{X}^{2}}}\]

\[Z=\sqrt{{{R}^{2}}+{{\left( {{X}_{C}}-{{X}_{L}} \right)}^{2}}}\Omega \]

The phase difference between voltage and current,

\[\phi ={{\tan }^{-1}}\left[ \frac{X}{R} \right]\]

\[{{\tan }^{-1}}\left[ \frac{{{X}_{L}}-{{X}_{C}}}{R} \right]\]

The power taken by the circuit,

\[P=VI\cos \phi \text{    Watts}\]

Power factor of the given circuit is $\cos \phi$ leading.

Case (iii): X_L= X_C

Figure (4): RLC Series Circuit Phasor Diagram when X_L = X_C.

From the phasor diagram shown in figure (4), the net reactance of the circuit for the given condition X_L= X_C is zero. The circuit behaves like a resistive circuit.

Net reactance,

\[X={{X}_{L}}-{{X}_{C}}\]

\[X=0\]

Impedance,

\[Z=\sqrt{{{R}^{2}}+{{X}^{2}}}\]

\[Z=\sqrt{{{R}^{2}}+0}=R\Omega \]

Power taken by the circuit,

\[P=VI\cos \phi \text{    Watts}\]

The phase difference between voltage and current is zero. Thus,

\[\phi = 0\]

Since the current is in phase with voltage, the power factor $\cos \phi$ is unity.

The post What is RLC Series Circuit? Circuit Diagram, Phasor Diagram, Derivation & Formula appeared first on ElectricalWorkbook.

Figure (1): RC Series Circuit.

An RC series circuit consisting of a resistor ‘R’ in series with a capacitor ‘C’ connected to an A.C supply as shown in figure (l).

Application of Kirchhoff’s voltage law to the circuit shown in figure (l), we get,

\[V={{V}_{R}}+{{V}_{C}}\]

Where,

V_R = Voltage drop across resistor = IR

V_C = Voltage drop across capacitor = IX_c

Figure (2): RC Series Circuit Phasor Diagram.

The phasor diagram is drawn taking current ‘I’ as the reference. The voltage drop V_R will be in phase with current I and voltage drop V_C will lagging current I by 90º. The phasor diagram is as shown in figure (2).

From the phasor diagram, we have,

\[{{V}^{2}}=V_{R}^{2}+V_{C}^{2}\]

\[={{\left( IR \right)}^{2}}+{{\left( I{{X}_{C}} \right)}^{2}}\]

\[={{I}^{2}}\left( {{R}^{2}}+X_{C}^{2} \right)\]

\[V=\sqrt{{{I}^{2}}\left( {{R}^{2}}+X_{C}^{2} \right)}\]

\[=L\sqrt{\left( {{R}^{2}}+X_{C}^{2} \right)}=IZ\]

Where

\[Z=\sqrt{\left( {{R}^{2}}+X_{C}^{2} \right)}\]

Figure (3): RC Series Circuit Impedance Triangle.

The phase angle difference $\phi$ is given by,

\[\tan \phi =\frac{{{V}_{C}}}{{{V}_{R}}}=\frac{I{{X}_{C}}}{IR}=\frac{{{X}_{C}}}{R}\]

\[\phi ={{\tan }^{-1}}\left( \frac{{{X}_{C}}}{R} \right)\]

Power factor,

\[\cos \phi =\frac{{{V}_{R}}}{V}=\frac{IR}{IZ}=\frac{R}{Z}\]

Total power,

P = VI cosϕ watts

The post What is RC Series Circuit? Circuit Diagram, Phasor Diagram, Derivation & Formula appeared first on ElectricalWorkbook.

Figure (1): RL Series Circuit.

An RL series circuit consisting of a resistor of ‘R’ Ohm in series with an inductance of ‘L’ Henrys connected to an A.C supply as shown in figure (l).

Applying Kirchhoff’s voltage law to the circuit shown in figure (1), we get,

\[V={{V}_{R}}+{{V}_{L}}\]

Where,

V = Source voltage

V_R = Voltage drop across resistor = IR

V_L = Voltage drop across inductor IX_L

Figure (2): RL Series Circuit Phasor Diagram.

The phasor diagram is drawn by taking the current ‘I’ as reference phasor as shown in figure (2).

The voltage drop ‘V_R‘ is in phase with current I since R is a pure resistance and voltage drop ‘V_L‘ leads current ‘I’ by 90º since L is a pure inductance.

From the phasor diagram, we have,

\[{{V}^{2}}=V_{R}^{2}+V_{L}^{2}\]

\[=\sqrt{V_{R}^{2}+V_{L}^{2}}\]

\[=\sqrt{{{\left( IR \right)}^{2}}+{{\left( I{{X}_{L}} \right)}^{2}}}=I\sqrt{R_{{}}^{2}+X_{L}^{2}}\]

\[V=IZ\]

Where, Z = Impedance in ohms $=\sqrt{R_{{}}^{2}+X_{L}^{2}}$

Figure (3): RL Series Circuit Impedance Triangle.

The phase difference angle $\phi$ can be determined from impedance triangle as shown in figure (3).

\[\tan \phi =\frac{AB}{OA}\]

\[\tan \phi =\frac{{{X}_{L}}}{R}\]

\[\phi ={{\tan }^{-1}}\frac{{{X}_{L}}}{R}\]

The power factor of the circuit is given by $\cos \phi$, since it is the cosine function of the phase angle between voltage and current.

\[\cos \phi =\frac{R}{Z}\]

Figure (1): RL Series Circuit Waveforms.

Let applied voltage, v = V_m sinωt

Then, equation of current will be,

\[i={{I}_{m}}\sin \left( \omega t-\phi  \right)\]

\[P=vi\]

\[=\left( {{V}_{m}}\sin \omega t \right)\left( {{I}_{m}}\sin \left( \omega t-\phi  \right) \right)\]

\[=\frac{1}{2}{{V}_{m}}{{I}_{m}}\left[ 2\sin \omega t\sin \left( \omega t-\phi  \right) \right]\]

\[=\frac{{{V}_{m}}{{I}_{m}}}{2}\left[ \cos \phi -\cos \left( 2\omega t-\phi  \right) \right]\]

\[=\frac{{{V}_{m}}{{I}_{m}}}{2}\cos \phi -\frac{{{V}_{m}}{{I}_{m}}}{2}\cos \left( 2\omega t-\phi  \right)\]

In the above expression the first term $\frac{{{V}_{m}}{{I}_{m}}}{2}\cos \phi $ represents the steady power, since V_m, I_m and are fixed in magnitude. The second term $\frac{{{V}_{m}}{{I}_{m}}}{2}\cos \left( 2\omega t-\phi  \right)$ represents the fluctuating power, which is zero over one full cycle.

The average power (or) total power,

\[P=\frac{{{V}_{m}}{{I}_{m}}}{2}\cos \phi\]

\[=\left( \frac{{{V}_{m}}}{\sqrt{2}} \right)\left( \frac{{{I}_{m}}}{\sqrt{2}} \right)\cos \phi \]

\[=VI\cos \phi \]

Where, V and I are r.m.s values of voltage and current.

The post What is RL Series Circuit? Circuit Diagram, Phasor Diagram, Derivation & Formula appeared first on ElectricalWorkbook.

(a) Circuit Diagram

(b) Phasor Diagram

Figure 1: Parallel Resonance Circuit.

In a parallel resonant circuit, the inductor L and capacitor C are connected in parallel as shown in Fig. 1 (a). The circuit current consists of two branch currents I₁ and I₂. The inductive current I₁ lags the voltage E by 90°. On the other hand the capacitive current I₂ leads the voltage E by 90°. These currents are 180° out of phase as shown in Fig. 1 (b). The total current I equals the resultant of these current components.

i.e.

\[I={{I}_{1}}+{{I}_{2}}\]

\[I=\frac{E}{Z}\]

If X_L and X_C are inductive and capacitive reactances then,

\[Z=\frac{{{X}_{1}}.{{X}_{2}}}{j{{X}_{1}}-{{X}_{2}}}\]

Also

\[Z=\frac{j\omega L.\frac{1}{j\omega C}}{j\left( \omega L-\frac{1}{\omega C} \right)} …(1)\]

At resonant frequency f_r,

\[\omega L=\frac{1}{\omega C}…(2)\]

Substituting this value in Eq. 1, we obtain,

\[Z=\frac{L/C}{0}=\infty \]

Solving Eq. 2

\[\omega L=\frac{1}{\omega C}\]

\[{{f}_{r}}=\frac{1}{2\pi \sqrt{LC}}\]

In practice, the inductance L always has a small internal resistance which must be taken into account. The impedance of the circuit including R is, therefore, given by

\[Z=\frac{\left( R+j\omega L \right)\frac{1}{j\omega C}}{R+j\left( \omega L-\frac{1}{\omega C} \right)}…(3)\]

At resonant frequency f_r, R << ωL. Therefore it can be neglected from the numerator.

Also

\[\omega L=\frac{1}{\omega C}\]

Substituting these values in Eq. 3 gives the impedance of a parallel resonant circuit as,

\[Z=\frac{L/C}{R}\]

\[Z=\frac{L}{CR}=\frac{{{\omega }_{r}}L}{{{\omega }_{r}}CR}={{\omega }_{r}}.L.Q\]

And resonant frequency

\[{{f}_{r}}=\frac{1}{2\pi \sqrt{LC}}\]

At resonance, the circuit offers maximum impedance. This impedance falls above and below the resonant frequency. To understand about variation of impedance of a parallel resonant circuit, consider Eq. (3) once again

\[Z=\frac{\left( R+j\omega L \right)\frac{1}{j\omega C}}{R+j\left( \omega L-\frac{1}{\omega C} \right)}\]

The denominator of this expression gives the impedance of a circuit in which elements L, C and R and connected in series. Thus if we denote this impedance as Z_S, (Since, R << jωL) then Eq. (3) may be rewritten as

\[Z=\frac{\left( R+j\omega L \right)\frac{1}{j\omega C}\approx \frac{L/C}{{{Z}_{S}}}}{{{Z}_{S}}}\]

The impedance Z of a parallel L, C and R circuit varies inversely with the series impedance Z_S of the same circuit. The plot of the impedance of a parallel circuit is then just the inverted form of the plot of impedance of series circuit. The magnification factor Q of a series resonant circuit has been defined as the ratio of the voltage across inductive reactance to the voltage across resistor R. In a parallel resonant circuit, the voltage across L and C is same as the signal voltage E and the magnification factor is defined as ratio between the circulating current in inductance (I_C) or capacitance (I_C) to the current I drawn from the signal source.

Thus Q of a parallel resonant circuit is given as,

\[Q=\frac{{{I}_{L}}}{I}=\frac{{{I}_{C}}}{I}\]

Now

\[{{I}_{C}}=\frac{E}{{{X}_{C}}}\]

\[{{I}_{L}}=\frac{E}{{{X}_{L}}}\]

\[ I=\frac{E}{Z}\]

Therefore,

\[Q=\frac{{{I}_{C}}}{I}=\frac{E}{{{X}_{C}}}\div \frac{E}{Z}\]

\[=\frac{E.\omega C}{E}\times \frac{L}{CR}=\frac{\omega L}{R}\]

Similarly,

\[Q=\frac{{{I}_{L}}}{I}=\frac{E}{{{X}_{C}}}\div \frac{E}{L/CR}\]

\[=\frac{E}{\omega L}\times \frac{L}{ECR}=\frac{1}{\omega CR}\]

Thus,

\[Q=\frac{\omega L}{R}=\frac{1}{\omega CR}…(4)\]

From Eq. (4), we find that magnification factor of a parallel resonant circuit is given by the same expression as that of a series resonant circuit.

Fig. 2. Plot of impedance/frequency for a  parallel resonant circuit.

The impedance versus frequency curve for the parallel circuit has the same general shape as the current/frequency of a series circuit and is shown in Fig. 2. The impedance is found to be maximum at resonance but decreases above or below resonance. If the internal resistance of the circuit is small, the impedance is large but shows a sharp decrease on both sides of the resonance frequency. The circuit is highly selective. If the internal resistance of the inductance is large, the impedance at resonance is low and impedance curve is flat.

Bandwidth of Parallel Resonance Circuit

Fig. 3. Plot of voltage/frequency for a  parallel resonant circuit.

If a current of varying frequency is fed to this circuit, the voltage developing across the tuned circuit will be different at different frequencies. At f_r , the voltage developed will be the highest because the impedance is highest while at other frequencies, the voltage falls. This is because of fall in the circuit impedance at those frequencies. Fig. 3 shows a plot of voltage/frequency for a parallel circuit. The bandwidth may be found out by marking the frequencies at which the voltage falls to 70.7

\[BW=\frac{{{f}_{r}}}{Q}\]

The post What is Parallel Resonance? Circuit Diagram, Phasor Diagram & Derivation appeared first on ElectricalWorkbook.

Figure 1: Unijunction Transistor (UJT).

A UJT can be conveniently considered as a bar or strip of high resistivity N-type silicon commonly called the base. Two contacts B₁ and B₂ are attached to it at opposite ends. A thin aluminum wire is alloyed at the middle of base to form a NP rectifying junction as shown in Fig. 1 (a). The connection brought from the aluminum P region is called the emitter. Fig. 1 (b) gives the circuit symbol of a unijunction transistor.

The construction of a UJT is similar to that of a JFET. The principal difference between the two is that the JFET has a much larger junction area compared to the UJT. Also, while the UJT is operated with the forward bias emitter junction, the JFET is always operated with gate-source junction reversed biased.

Unijunction Transistor (UJT) Characteristics 

When DC voltage is connected between base 2 and base 1, as shown in Fig. 2 (a), the N-type bar behaves as a resistance and a current flows between base 2 and base 1 such that

\[{{I}_{B2}}= & \frac{{{V}_{BB}}}{{{R}_{B2}}+{{R}_{B1}}}\]

Where R_B2 is the resistance of the bar measured between the junction and the terminal B₂ and R_B1 is the resistance offered by the region extending between junction and B₁ as shown in Fig. 2 (b).

Due to this current flow, there is a uniform voltage distribution between the points B₁ and B₂. This potential distribution raises the potential of the mid-region of the bar with respect to the lower point B₁ which is at zero potential. In this situation, if the emitter point is connected to ground (i.e. its potential V_EE is made zero), then the potential of the N-region adjoining the P-N junction will be positive with respect to the P-region and the P-N junction is reverse biased. This potential cannot however be measured since meter load cannot be placed at the mid-region of the bar.

Fig. 3: Static characteristics of a UJT

Reverse biasing of the junction leads to a flow of reverse leakage current in the emitter as shown by dotted line in the static characteristics of the devices in Fig. 3.

If a voltage V_E is applied between emitter and base 1 as shown in Fig. 2 (a), the potential of the emitter will be raised and the reverse bias across the P-N junction which is the difference between voltages at the emitter and the mid-region of the bar is lowered. Lowering the reverse bias decreases the reverse leakage current. When the emitter potential V_E equals the potential of the mid-region of the bar, reverse bias is completely neutralized and tie reverse leakage current becomes zero.

A further increase in the emitter voltage V_E causes the junction to be forward biased. When the emitter voltage overcomes the potential barrier, the emitter current shows a sharp increase. This point is marked as the peak point in Fig. 3 and the emitter voltage and current corresponding to the peak point are called the peak voltage and peak current. The emitter current completes its path through the lower region of the bar.

Since the N-channel region is of high resistivity, it has a small number of free electrons whereas there are large numbers of holes in the P-region. Thus, most of the emitter current flow results due to movement of holes. These holes cross over the junction and move through the region R_B1. The presence of large number of holes in the lower region of the bar reduces the resistance R_B1 to a very low value. This results in a sharp increase in the emitter current, voltage drop across emitter resistance R_E also increases and potential of the emitter falls. Thus we obtain a region of characteristic in which an increase of current flow is accompanied by a drop in the emitter potential. Such a region is called the negative resistance region and is shown in Fig. 3.

The negative resistance region continues till a minimum emitter potential is reached. This is termed as the valley point and is marked in Fig. 3. Beyond the valley point, an increase in current is accompanied by a corresponding increase in emitter voltage and is termed as saturation region. The region of characteristic to the left of the peak point is called the cut-off region. Important applications of UJTs use the negative resistance region of characteristic.

The post What is Unijunction Transistor (UJT)? Working, Circuit Diagram, Symbol & Characteristics appeared first on ElectricalWorkbook.

Fig. 1: Shunt Resistor.

Shunts for D.C. Circuits

Precise low resistances of an accuracy of 0.1

1. Permanent and simple construction.
2. Adequate and well designed current and potential terminals.
3. Low temperature coefficient.
4. Small thermoelectric e.m.f.
5. Adequate cooling.

Manganin is most commonly used material for shunts. Constantan and Therlo are also used by some people for shunts. All the shunts have four terminals, two for attachement of the current carrying leads and two for measurement of potential drop across it. The first pair of terminals are current terminals, while the second pair are potential terminals. It uses manganin strip or strips hard soldered into copper end pieces which are shot soldered into copper blocks (Fig. 1). The current terminals are made on the copper blocks at the ends remote from the resistance strip to ensure a uniform current density in the region of the points of connections to the measurement circuit. To ensure a fixed potential drop across the shunt, the potential terminals must be made nearer to the resistance where the current density is uniform.

To keep the temperaure within limit, oil and forced cooling may be adopted. For heavier power rating the resistance strips are bent to a U-shape and immersed in oil in a container. The oil may be stirred by a motor-driven propeller. For even large power oil is cooled by circulating cold water through a helical tube in it.

Shunts for A.C. Circuits

The shunts for A.C. circuits should be non-inductive. The bifilar method can be used for this purpose. For heavy current shunts two concentric cylinders of manganin and carrying currents in opposite directions are used. The two cylinders are joined together by silver soldering a common copper ring at one end. At the other end, the two cylinders are joined similarly to two separate copper rings attached to copper rods leading to the current terminals. This can be used for frequencies upto 1 kHz. But due to the development of accurate transformers the demands of heavy current AC. shunts have been decreased.

The post What is Shunt Resistor? Definition, Diagram & Types appeared first on ElectricalWorkbook.

The phasors representing different alternating quantities of the same frequency rotate in an anti-clockwise direction with the same angular velocity (ω = 2πf). As such they maintain a fixed position relative to each other. Therefore, a phasor diagram can be considered as a still picture of these phasors in one particular position.

As an example, let us consider the case of the e.m.f.s in two single-turn coils A and B shown in Fig. 1.

Fig. 1: Two alternating quantities.

(a)

(b)

Fig. 1: Phasor diagram for two alternating quantities.

If the wave for the e.m.f. in coil A is supposed to pass upward in positive direction through zero at the instant when t = 0, then at the same instant, the wave for the e.m.f. in the coil B already attains some positive value because of its advancement through an angle a from its zero value (Fig. 2 a). This can be shown with the help of phasors in the phasor diagram as illustrated in Fig. 2 (b). The angle a between two phasors is obviously the phase difference between the two e.m.f.s.

Following few points should be noted in connection with the phasor diagrams:

1. X and Y axes are fixed in space. Therefore, it is not necessary to include them in the diagram.
2. The phasors are drawn normally to represent r.m.s. values.
3. The phasor chosen as a reference phasor is drawn in the horizontal position (merely for convenience) e.g. the phasor E_mA in Fig. 2 (b) is the reference phasor.
4. Since the phasors representing different alternating quantities are assumed to rotate in the counter clockwise direction, the phasors ahead in this direction from a given phasor are said to lead the given phasor, while those behind are said to lag the given phasor. e.g. in Fig. 2 (b), the phasor E_mB leads the phasor E_mA by an angle α. The angle between two phasors represents the phase difference between two alternating quantities.
5. In order to distinguish between different alternating quantities like current, voltage or flux, different types of arrow heads may be used. e.g. the current phasors may be drawn with closed arrow heads while the voltage phasors with open arrow heads.

In this way, when different alternating quantities of the same frequency are represented by phasors in the same phasor diagram. their addition and subtraction becomes simple. It is similar to addition and subtraction of vectors in mechanics.

The post What is Phasor Diagram? Definition, Theory & Steps appeared first on ElectricalWorkbook.

The load on a three-phase system may be either star or delta connected irrespective of the type of connection for armature windings of the alternator. If all phase impedances of the three-phase load are exactly identical in respect of magnitude and their nature, it is said to be a balanced, three-phase load.

For example. if each phase of the three-phase load has a resistance of 10 Ω and inductive reactance of 25 Ω it will form a balanced, three-phase load. However, ¡f one of the phases has a capacitive reactance of 25 Ω in place of inductive reactance. then inspite of equal impedances in all the phases, the load will not be the balanced one. In practice. a three-phase motor connected across the supply forms a balanced load (Fig. 1).

Fig. 1: Loading of a three-phase system

The lighting and heating loads which are resistive in nature are normally connected between one line and neutral. The electricity authorities always try to distribute such single-phase loads on all the three phases as equally as possible. Thus, in such condition, all these single-phase loads also form a balanced. star-connected load.

Three Phase Balanced System

A three-phase system is said to be balanced when it possesses the following characteristics :

(i) The e.m.f.s (voltages) for three phases are equal and phase displaced by 120 electrical degrees.

(ii) The impedance in any one phase is identical to that in either of the other two phases.

(iii) The resulting currents in different phases are equal and have same phase angles. Or, in other words, they are also phase displaced from each other by 120 electrical degrees.

(iv) Equal power and equal reactive power flow in each phase.

Definite efforts are made to keep the three-phase system in balanced condition by using balanced loading. It is important to note that all the relations which are developed or conclusions which are reached in respect of three-phase systems are entirely based on the assumption that these systems are balanced.

The post What is Balanced Load? appeared first on ElectricalWorkbook.