Found 451 Articles for Electron

Thevenin’s Theorem is used, where it is desired to determine the current through or voltage across any one circuit element without going through the complex method of solving a set of network equations.Statement of Thevenin’s TheoremAny two terminal bilateral linear dc circuit can be replaced by an equivalent circuit consisting of voltage source in series with a resistance, the voltage source being the open circuited voltage across the open circuited load terminals and the resistance being the internal resistance of the source network looking through the open circuited load terminals.Explanation of Thevenin’s TheoremStep 1 – Remove the load resistor (RL) ... Read More

A practical voltage source consists of an ideal voltage source in series with an internal resistance (for an ideal voltage source, this internal resistance being zero, so that the output voltage becomes independent of the load current) While a practical current source consists of an ideal current source in parallel with an internal resistance (for an ideal current source, this parallel resistance is infinity).The practical voltage and current sources are mutually transferable i.e. a practical voltage source can be converted into a practical current source and vice-versa.Voltage to Current Source TransformationConsider a practical voltage of V volts having a series ... Read More

Consider the circuit consisting of R, L and C connected in series across a supply voltage of V (RMS) volts. The resulting current I (RMS) is flowing in the circuit. Since the R, L and C are connected in series, thus current is same through all the three elements. For the convenience of the analysis, the current can be taken as reference phasor. Therefore, $$\mathrm{Voltage\:acorss\:\mathit{R}, \mathit{V}_{R}=\mathit{IR}}$$$$\mathrm{Voltage\:acorss\:\mathit{L}, \mathit{V}_{L}=\mathit{IX}_{L}}$$$$\mathrm{Voltage\:acorss\:\mathit{C}, \mathit{V}_{C}=\mathit{IX}_{c}}$$Where, XL = jωL = Inductive Reactince,  Xc = 1/jωC = Capacitive reactance. VR  is in phase with I. VL  is leading the current I by 90°. VC  is lagging the I by 90°.The total voltage ... Read More

A series-parallel circuitis a combination of series and parallel circuits. In this circuit some of the elements are connected in series fashion and some are in parallel.In the circuit shown below, we can see that resistors R2 and R3 are connected in parallel with each other and that both are connected in series with R1.To solve such circuits, first reduce the parallel branches to an equivalent series branch and then solve the circuit as a simple series circuit.Here, RP is equivalent resistance of parallel combination given by, $$\mathrm{\mathit{R}_{p}=\frac{\mathit{R}_{2}\mathit{R}_{3}}{\mathit{R}_{2}+\mathit{R}_{3}}}$$Total circuit resistance (RT) is given by, $$\mathrm{\mathit{R}_{r}=\mathit{R}_{1}+\mathit{R}_{p}=\mathit{R}_{1}+\frac{\mathit{R}_{2}\mathit{R}_{3}}{\mathit{R}_{2}+\mathit{R}_{3}}}$$Voltage across the parallel combination is ... Read More

The resistors are said to be connected in series, when they are joined end to end so that there is only one path for the current to flow.ExplanationLet the three pure resistors R1, R2 and R3 be connected in series against a DC voltage source V as shown in the circuit.Referring the circuit it can be written that$$\mathrm{\mathit{V}\:=\:\mathit{V}_{1}+\mathit{V}_{2}+\mathit{V}_{3}\:\:\:\:…(1)}$$Where V1, V2 and V3 being the voltage drops against individual resistors.Assuming I to be the total current in the circuit and R being the equivalent resistance of all the series resistors. Hence, the equation (1) can be written as$$\mathrm{\mathit{IR}=\mathit{IR}_{1}+\mathit{IR}_{2}+\mathit{IR}_{3}}$$$$\mathrm{\Rightarrow\:\mathit{R}=\mathit{R}_{1}+\mathit{R}_{2}+\mathit{R}_{3}\:\:\:\:…(2)}$$Thus, the equation (2) ... Read More

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