Found 1006 Articles for Electronics & Electrical

When one end of each resistor is joined to a common point and the other end of each resistor is joined to another common point so that there are as many paths for current flow as the number of resistors, it is called as a parallel circuit.The below circuit shows the connection of three resistors in parallel across a DC voltage source V. Let the circuit current be 𝐼 while the branch currents I1, I2 and I3 respectively. The voltage drop in each branch being same, so by Ohm’s law, we can write, $$\mathrm{\mathit{V}=\mathit{I}_{1}\mathit{R}_{1}=\mathit{I}_{2}\mathit{R}_{2}=\mathit{I}_{3}\mathit{R}_{3}}$$Also, by referring the circuit, $$\mathrm{\mathit{I}=\mathit{I}_{1}+\mathit{I}_{2}+\mathit{I}_{3}}$$$$\mathrm{\Rightarrow\frac{\mathit{V}}{\mathit{R}_{p}}=\frac{\mathit{V}}{\mathit{R}_{1}}+\frac{\mathit{V}}{\mathit{R}_{2}}+\frac{\mathit{V}}{\mathit{R}_{3}}}$$Where, RP ... Read More

Consider a parallel RLC circuit shown in the figure, where the resistor R, inductor L and capacitor C are connected in parallel and I (RMS) being the total supply current. In a parallel circuit, the voltage V (RMS) across each of the three elements remain same. Hence, for convenience, the voltage may be taken as reference phasor.Here, $$\mathrm{\mathit{V}=\mathit{IZ}=\frac{\mathit{I}}{\mathit{Y}}}$$Where, Z= Total impedance of the parallel circuit, Y=1/Z= Admittance of the parallel circuit.The admittance of the parallel circuit is given by, $$\mathrm{\mathit{Y}=\frac{1}{\mathit{R}}+\frac{1}{\mathit{j\omega L}}+\mathit{j\omega C}=\frac{1}{\mathit{R}}+ {\mathit{j}}(\mathit{\omega C}-\frac{1}{\mathit{\omega L}})=\mathit{G}+\mathit{jB}}$$Where, G=1/R= Conductance of the circuit, B=1/X= Susceptance of the circuit, $$\mathrm{Magnitude\:of\:admittance, |\mathit{Y}|=\sqrt{(\frac{1}{\mathit{R}})^{2}+(\mathit{\omega C}-\frac{1}{\mathit{\omega L}})^{2}}}$$$$\mathrm{Phase\:angle\:of\:admittance, \:\varphi=\tan^{-1}(\frac{\mathit{\omega ... Read More

When the resistances are connected with each other such that one end of each resistance is joined to a common point and the other end of each resistance is joined to another common point so that the number paths for the current flow is equal to the number of resistances, it is called a parallel circuit.ExplanationConsider three resistors R1, R2 and R3 connected across a source of voltage V as shown in the circuit diagram. The total current (I) divides in three parts – I1 flowing through R1, I2 flowing through R2 and I3 flowing through R3. As, it can ... Read More

Nodal Analysis is a method for determining the branch currents in a circuit. In this method, one of the nodes is taken as the reference node. The potentials of all the nodes in the circuit are measured with respect to this reference node.The nodal analysis is based on the Kirchhoff’s Current Law, which states that "the algebraic sum of incoming currents and outgoing currents at a node is equal to zero".$$\mathrm{\sum\:\mathit{I}_{incoming}\:+\:\sum\:\mathit{I}_{outgoing}=0}$$Node – A node is a point in a network where two or more circuit elements meet.Junction – A junction is point where three or more circuit elements meet.In the ... Read More

In this method, Kirchhoff’s voltage law is applied to a network to write mesh equations in terms of mesh currents. The branch currents are then found by taking the algebraic sum of the mesh currents which are common to that branch.Kirchhoff’s Voltage LawThe Kirchhoff’s voltage law (KVL) states that, the algebraic sum of all the emfs and voltage drops is equal to zero in a mesh i.e.$$\mathrm{\sum\:emfs\:+\:\sum\:Voltage\:Drops = 0}$$Mesh − A mesh is a most elementary form of a loop, which cannot be further divided into other loops i.e. a mesh does not have any inner loop.ExplanationEach mesh is assigned ... Read More

MagnetismIn the ancient times, people believed that the invisible forces of magnetism was purely a magical quantity. However, with the increasing scientific knowledge over the passing centuries, magnetism assumed a larger and larger role. Today the magnetism has attained a place of pride in electrical engineering. Without the magnetism, it is impossible to operated electrical devices like generators, motors, transformers, TV, radio, telephone etc. Therefore, electrical engineering is much dependent on magnetism.Magnetic polesA magnet has two poles viz. North Pole and South Pole. In order to determine the polarity of a magnet, suspend it at its centre, then the magnet ... Read More

A voltage divider or potential divider is a series circuit that is used to provide more than one reduced voltages from a single source of voltage.Consider a circuit of voltage divider as shown below, in which two reduced voltages V1 and V2 are obtained from a single input voltage source of V volts. Since no load is connected to circuit, it is called unloaded voltage divider.Refer the circuit of unloaded voltage divider, $$\mathrm{Circuit\:Current, I= \frac{V}{R_{1}+{R_{2}}}=\frac{V}{R_{eq}}}\:\:\:… (1)$$        Where, Req=R1 + R2= Total resistance of voltage dividerTherefore, $$\mathrm{V_{1}=IR_{1}=\frac{V}{R_{eq}}×R_{1}=V\frac{R_{1}}{R_{eq}}}\:\:\:… (2)$$$$\mathrm{V_{2}=IR_{2}=\frac{V}{R_{eq}}×R_{2}=V\frac{R_{2}}{R_{eq}}}\:\:\:… (3)$$Hence, equation (2) and (3) shows that, the voltage drop ... Read More

A resistor is a circuit element that opposes the flow of electric current in the circuit by virtue of its property called resistance.According to I-V characteristic, the resistors may be classified in two categories viz.Linear ResistorNon-Linear ResistorOhm’s LawIf the physical conditions are constant, then the ratio of applied voltage across a conductor to the current through it remains constant and equal to the resistance of the conductor.$$\mathrm{R=\frac{V}{I}\:or\:V}=IR$$$$\mathrm{∴V\:∝\:I}$$Therefore, I-V characteristic is a straight line passing through the origin at all times.Linear ResistorA linear resistor is defined as a two terminal circuit element which satisfies Ohm’s law i.e. the voltage across the ... Read More

Consider the circuit containing a pure inductive coil of inductance L Henry. When an alternating voltage V (RMS) is applied across the coil, an alternating current I (RMS) will flow through the circuit. Due to this alternating current, a back emf (e) is induced in the coil due to inductance of it. This back emf at every instant opposes the any change in current through the coil.Let the applied alternating voltage is$$\mathrm{u=V_{m}sin\:\omega t}\:\:\:… (1)$$The back emf (e) induced in the inductor coil is given by, $$\mathrm{e=L \frac{di}{dt}}\:\:\:… (2)$$Since, there is no ohmic drop, thus the applied voltage has to overcome ... Read More

Power or Electric PowerThe rate at which work is done in an electric circuit is called as electric power. In other word, the work done per unit time is termed as electric power. It is denoted p or P.Formula and Unit of PowerWhen voltage is applied across a resistor, it causes current to flow through it. Therefore, work is being done in moving the electrons through the resistor in a unit time is called the electric power.Referring the above figure, $$\mathrm{V=\frac{work}{Q}}$$$$\mathrm{\Rightarrow work(W)=VQ=VIt}$$As, the power is defined as work done per unit time i.e.$$\mathrm{Power(P)=\frac{work\:done\:in\:electric\:circuit(W)}{Time(t)}=\frac{VIt}{t}}$$$$\mathrm{(∵V=IR\:or\:I=\frac{V}{R})}$$$$\mathrm{∴P=VI=I^2R=\frac{V^2}{R}}$$The above three formulae are equally valid for ... Read More