# Chapter 27: A.c. bridges

### Example 1, page no. 485

In :
from __future__ import division
import math
import cmath
#initializing  the  variables:
R2  =  2500;#  in  ohms
C2  =  0.2E-6;#  IN  fARADS
R3 = 1;
R4 = 1;
w = 2000*math.pi;
#calculation:
Rx = R4*(1 + w*w*C2*C2*R2*R2)/(R2*R3*w*w*C2*C2)
Cx = R3*C2/(R4*(1 + w*w*C2*C2*R2*R2))

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Resistance  Rx  = R4(1 + w*w*C2*C2*R2*R2)/(R2*R3*w*w*C2*C2) and Capacitance Cx = R3*C2/(R4*(1 + w*w*C2*C2*R2*R2))"
print  "\n  (b)at balance Rx = ",round(Rx/1000,2),"KOhm and Cx = ", round(Cx*1E9,2),"nF\n"


Result

(a)Resistance  Rx  = R4(1 + w*w*C2*C2*R2*R2)/(R2*R3*w*w*C2*C2) and Capacitance Cx = R3*C2/(R4*(1 + w*w*C2*C2*R2*R2))

(b)at balance Rx =  2.75 KOhm and Cx =  18.4 nF

### Example 2, page no. 487

In :
from __future__ import division
import math
import cmath
#initializing  the  variables:
R2  =  30000;#  in  ohms
R3  =  30000;#  in  ohms
R4  =  1000;#  in  ohms
C2  =  1e-9;#  IN  fARADS
C3  =  1e-9;#  IN  fARADS

#calculation:
#the  bridge  is  balanced
R1  =  R4/((R3/R2)  +  (C2/C3))
#frequency,  f
f  =  1/(2*math.pi*((C2*C3*R2*R3)**0.5))

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Resistance  R1  =  ",R1,"  ohm\n"
print  "\n  (b)frequency,  f  is  ",round(f,2),"Hz\n"


Result

(a)Resistance  R1  =   500.0   ohm

(b)frequency,  f  is   5305.16 Hz

### Example 3, page no. 487

In :
from __future__ import division
import math
import cmath
#initializing  the  variables:
R3  =  600;#  in  ohms
R4  =  200;#  in  ohms
C2  =  0.2e-6;#  IN  fARADS
C3  =  4000e-12;#  IN  fARADS
f  =  1500;#in  Hz

#calculation:
#the  bridge  is  balanced
#Resistance,  Rx
Rx  =  R4*C3/C2
#Capacitance,  Cx
Cx  =  C2*R3/R4
#Phase  angle
phi  =  math.atan(1/(2*math.pi*f*Cx*Rx))
phid  =  phi*180/math.pi#  in  degrees
#Power  factor  of  capacitor
Pc  =  math.cos(phi)
#Loss  angle,
de  =  90  -  phid

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Resistance  Rx  =  ",round(Rx,2),"  ohm\n"
print  "\n  (b)capacitance,  Cx  is  ",round(Cx*1E9,2),"pFarad\n"
print  "\n  (c)phasor  diagram  =  ",round(phid,2),"deg lead "
print  "\n  (d)power  factor  is  ",round(Pc,2),"  \n"
print  "\n  (e)Loss  angle  =  ",round(de,2),"deg\n"


Result

(a)Resistance  Rx  =   4.0   ohm

(b)capacitance,  Cx  is   600.0 pFarad

(c)phasor  diagram  =   88.7 deg lead

(d)power  factor  is   0.02

(e)Loss  angle  =   1.3 deg