Resistance in Series Circuits

Series Circuit

• A series circuit is defined as a circuit that provides only one path for current between two points, so that the current is the same through each series resistor.
• There is no limit to the number of resistors that can be connected in series.
• The total resistance in a series circuit is the sum of each of the individual resistors: RT = R1 + R2 + R3 + … + Rn.

Parallel Circuit

• A parallel circuit is identified if there is more than one current path (branch) between two points, and if the voltage between those two points also appears across each of the branches.
• Each parallel path in a circuit is called a branch.
• The equivalent current distribution in a parallel circuit shows the current out of the source dividing when it gets to a point, and then coming back together at another point.

Unilateral Circuit

• A unilateral circuit is one whose properties or characteristics change with the direction of its operation.
• A diode rectifier is a unilateral circuit because it cannot perform rectification in both directions.

Passive and Active Networks

• A passive network is one that contains no source of e.m.f.
• An active network is one that contains one or more sources of e.m.f.

Circuit Elements

• Node is a junction in a circuit where two or more circuit elements are connected together.
• Branch is that part of a network that lies between two junctions.
• Loop is a closed path in a circuit in which no element or node is encountered more than once.
• Mesh is a loop that contains no other loop within it.

Kirchhoff's Mesh Law (KVL)

• Kirchhoff's Mesh Law or Voltage Law (KVL) states that the algebraic sum of the products of currents and resistances (IR) in each of the conductors in any closed path (or mesh) in a network plus the algebraic sum of the emfs in that path is zero.
• It can be stated as: in any closed electric circuit, the sum of potential drops (I.R) is equal to the sum of the impressed emfs.

Determinants and Cramer's Rule

• Determinants provide a simple and straightforward method for solving network equations through manipulation of their coefficients.
• The symbol |a b| / |c d| is called a determinant of the second order (or 2 × 2 determinant).
• The numbers a, b, c, and d are called the elements or constituents of the determinant.

Maxwell's Loop Current Method

• This method is particularly well-suited to coupled circuit solutions and employs a system of loop or mesh currents instead of branch currents.
• It eliminates a great deal of tedious work involved in the branch-current method and is best suited when energy sources are voltage sources rather than current sources.

Norton's Theorem

• Norton's theorem states that any two-terminal active network containing voltage sources and resistance, when viewed from its output terminals, is equivalent to a constant-current source and a parallel resistance.
• The equivalent current source is designated IN, and the equivalent resistance is designated RN.
• The voltage between any two points in a network is equal to ISC.Ri, where ISC is the short-circuit current between the two points and Ri is the resistance of the network as viewed from these points with all voltage sources being replaced by their internal resistances.

Maximum Power Transfer Theorem

• The theorem is applicable to all branches of electrical engineering, particularly useful for analyzing communication networks.
• The overall efficiency of a network supplying maximum power to any branch is 50 per cent.
• The application of this theorem to power transmission and distribution networks is limited because, in their case, the goal is high efficiency and not maximum power transfer.