# Elements Of Network

**Resistance**

V = RI

Here R is the resistance

Resistance, R =

where

ρ = resistivity of the material;

= length of the wire;

A = area of cross-section

Resistance varies with temperature

R* _{t}* = R

_{0}(1 + αΔT)

where ΔT = change in temperature

α = temperature coefficient of resistance

Series connection :

R_{eq} = R_{1} + R_{2} + R_{3} + ...... + R_{n}

Parallel connection :

** **

# Inductance

**Self inductance**

Coefficient of self inductance, where

N = no. of turns in coil

ϕ = flux; I = current

Its unit is henry (H)

induced emf self induced emf (e)

*e* =

*Energy stored by an inductor = *

** **

**Mutual inductance**

Coefficient of mutual inductance :

For coil 1 : M_{12}= ;

For coil 2 : M_{21} =

M_{12} = M_{21} = M

** **

**Coefficient of Coupling :**

K =

Mathematically, K =

Series combination :

L_{eq} = L_{1} + L_{2} + ......+ L_{n}

Parallel combination :

=

# Combination of Inductors with Mutual Inductance

**L**_{eq}= L_{1}+ L_{2}+ 2M- L
_{eq}= L_{1}+ L_{2}– 2M

**Capacitance**

Current through the capacitor,

Energy stored by a capacitor =

Series combination

Parallel combination

C_{eq} = C_{1} + C_{2} + C_{3} + ..... + C_{n}