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Elements Of Network

Resistance

V = RI

Here R is the resistance


Resistance, R = 
440.png 


where
ρ = resistivity of the material;

* = length of the wire;

A = area of cross-section


Resistance varies with temperature

Rt = R0 (1 + αΔT)

where ΔT = change in temperature

α = temperature coefficient of resistance


Series connection :

Req = R1 + R2 + R3 + ...... + Rn


Parallel connection :

445.png 

Inductance

Self inductance

Coefficient of self inductance, 450.png where

N = no. of turns in coil

ϕ = flux; I = current


Its unit is henry (H)

induced emf self induced emf (e)

e = 455.png

Energy stored by an inductor = 460.png

 

Mutual inductance

Coefficient of mutual inductance :

For coil 1 : M12465.png;


For coil 2 : M21 = 
470.png

M12 = M21 = M

 

Coefficient of Coupling :

K = 475.png 

Mathematically, K = 480.png 


Series combination :

Leq = L1 + L2 + ......+ Ln


Parallel combination :

485.png = 490.png

Combination of Inductors with Mutual Inductance

  1. 495.pngLeq = L1 + L2 + 2M
  2. 500.pngLeq = L1 + L2 – 2M
  3.  505.png510.png
  4. 515.png520.png

Capacitance

Current through the capacitor, 525.png 

Energy stored by a capacitor = 530.png 


Series combination

535.png 


Parallel combination

Ceq = C1 + C2 + C3 + ..... + Cn





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