PARALLEL CONNECTION OF ELEMENTS

PARALLEL CONNECTION OF ELEMENTS:

The parallel circuit is one in one in which several resistances are connected across one another in such a way that one terminal of each is connected to from a junction point while the remaining ends are also joined to from another junction point.

Resistances in parallel connection:

· consider a parallel circuit as shown in the figure in the parallel connection shown .The three resistances R1,R2,R3 are connected in parallel and combination is connected across a source of voltage'V' in parallel circuit the current passing through each resistance is different let total current drawn is 'i' ampere's

V=V1=V2=V3

i=i1+i2+i3 (i.e. KCL)

(V/R)=(V1/R1)+(V2/R2)+(V3/R3)

(V/R)=V((1/R1)+(1/R2)+(1/R3))

(1/R)=(1/R1)+(1/R2)+(1/R3)

· When 'n' resistances are connected in parallel

(1/R)=(1/R1)+(1/R2)+(1/R3)+.......................+(1/Rn)

· When the two resistances are connected in parallel

(1/R)=(1/R1)+(1/R2)

(1/R)=(R1+R2)/R1*R2

· Conductance(G): Conductance is reciprocal of resistance

G=(1/R)

Inductance in parallel connection:

· Consider the figure shows three inductance's L1,L2 and L3 are connected in parallel . The current flowing through L1,L2 and L3 are i1,i2 and i3 respectively .The voltage developed across inductance's are VL volts.

i=i1+i2+i3 & V=V1=V2=V3

(1/L)=(1/L1)+(1/L2)+(1/L3)

· When 'n' inductance's are connected in parallel

(1/L)=(1/L1)+(1/L2)+(1/L3)..............(1/Ln)

· Two inductance's are connected in parallel

(1/L)=(1/L1)+(1/L2)

(1/L)=(L1+L2)/L1*L2

L=L1*L2/(L1+L2)

Capacitances in parallel connection:

Consider the figure shows three capacitors C1,C 2and C3 are connected in parallel.The current flowing through capacitors C1,C2 and C3 are i1,i2 and i3 respectively and voltage developed across capacitors are 'VL' volts.