Voldate represents the work per unit charge (J/C) required to move the charges from one point to the other.


Resistance is determined by the physical dimensions and the resistivity ρ of the material of which the resistor is composed. For a bar of resistive material of length l and cross-sectional area A the resistance is given by $$R=\frac{\rho l}{A} =\frac{l}{\sigma A}$$ ρ [Ω·m] is the resistivity of the material, and σ [S/m] is the conductivity of the material.

Electric circuits


In the electric circuits,there are three parts of electric devices.Source provide the power,conductor like wire will transfer electric to the load,and the load will transform electric to other forms.

Circuit equations

An electric circuit may be described mathematically by ordinary differential equations.

All the linear equations are used to construct a line. A non-linear equation is such which does not form a straight line. It looks like a curve in a graph and has a variable slope value.

Equivalent circuit


Two elements represents the transformation of electric energy from nonelectric energy. EMF source and current source.





Resistance is an equivalent circuit element which represents the transformation of electric energy into nonelectric energy.
Resistance(R)\(R=\frac{du}{di}\) Conductance(g)\(g=\frac{di}{du}\)


An ideal inductor is an energy-storage circuit element (with no loss associated with it) representing the magnetic-field effect. $$L=\frac{d\psi }{di}$$ $$i(t)=\frac{1}{L}\int u(t)dt$$


An ideal capacitor is an energy-storage circuit element (with no loss associated with it) representing the electric-field effect. $$C=\frac{dq}{du}$$ $$u(t)=\frac{1}{C}\int i(t)dt$$

When elements have their own signs,if the current flow is opposite to it the whole power is on the contrary.

Circuit topology

Series connection

$$R_{eq}=R_{1}+R_{2}+R_{3}+R_{4}+R_{5}$$ $$L_{eq}=L_{1}+L_{2}+L_{3}$$ $$E_{eq}=E_{1}+E_{2}+E_{3}-E_{4}+E_{5}$$ $$g_{eq1}=g_{2}+g_{3}\qquad g_{eq2}=g_{eq1}+g_{1}$$ $$R_{eq1}=\frac{R_{2}R_{3}}{R_{2}+R_{3}}\qquad R_{eq2}=\frac{R_{1}R_{eq1}}{R_{1}+R_{eq1}}$$ $$\frac{1}{C_{eq}}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}$$ $$J_{eq}=J_{1}+J_{2}-J_{3}$$

Node & Junction

A node is a point at which two or more components or devices are connected together. The node can be called a junction point in the case of connecting of three or more wires.

Branch & Loop

A branch is a part of a circuit containing one element or several elements connected in series.Actually a element with two terminals can be seen as a branch. A loop is a closed path formed by starting at a node, passing through a set of nodes, and returning to the starting node without passing through any node more than once.

Star and delta connections

$$\left\{ \begin{aligned} & R_a&= & \frac{R_{ab}R_{ac}}{R_{ab}+R_{ac}+R_{bc}}&\\ & R_b&= & \frac{R_{ba}R_{bc}}{R_{ab}+R_{ac}+R_{bc}}&\\ & R_c&= & \frac{R_{cb}R_{ca}}{R_{ab}+R_{ac}+R_{bc}}&\\ \end{aligned} \right. \Leftrightarrow \left\{ \begin{aligned} & R_{ab}&= & \frac{R_aR_b+R_aR_c+R_bR_c}{R_c}&\\ & R_{ac}&= & \frac{R_aR_b+R_aR_c+R_bR_c}{R_b}&\\ & R_{bc}&= & \frac{R_aR_b+R_aR_c+R_bR_c}{R_a}&\\ \end{aligned} \right.$$