# Chapter 4 - Potentiometers¶

## Example 1 - pg 256¶

In :
#pg 256
#Example 4.1: Unknown resistor
#calculate the Unknown resistor
#given data :
Vd=0.83942;# volt-drop in V
emf=23*10**-6;# in V
Vds=1.01575;# volt-drop in V
Rs=0.10014;# in ohm
#calculations
Vdt=Vd-emf;# in V
I=Vds/Rs;
R=Vdt/I;
#results
print "Unknown resistor (ohm) = ",round(R,5)

Unknown resistor (ohm) =  0.08275


## Example 2 - pg 257¶

In :
#pg 257
#Example 4.2: emf and % error
#calculate the emf and % error
#given data :
l=50;# in cm
l1=70;# in cm
l2=65;# in cm
l3=43.5;# in cm
I=0.45;# in A
V=1.0183;# in V
V1=1.35;# in V
R=2;# in ohm
#calculations
Vpl=V/l;# in V/cm
emf=Vpl*l1;
Vr=Vpl*l2;
P_error1=((V1-Vr)/Vr)*100;
Ir=(Vpl*l3)/R;# in A
P_error2=((I-Ir)/Ir)*100;
#results
print "(a). emf of the cell,(V) = ",emf
print "(b). % error (high),(%) = ",round(P_error1,2)
print "(c). % error (high),(%) = ",round(P_error2,2)

(a). emf of the cell,(V) =  1.42562
(b). % error (high),(%) =  1.98
(c). % error (high),(%) =  1.59


## Example 3 - pg 258¶

In :
#pg 258
#Example 4.3.a: current and resistance
#calculate the current and resistance
#given
import numpy
from numpy import linalg
e1=1.0191;#V
r1=100.;#ohms
l=2;#m
e2=4;#V
#calculations and results
I=l/r1;#A
rh=(e2/I)-r1;#
print 'part a '
print "current is (A)=",I
print "resistance is (ohm)=",rh
e1=4;#V
e2=1.0191;#V
R1=100;#OHM
R2=49.045;#OHMS
r3=R1-R2;#ohms
rg=50;#ohms
r4=200;#ohms
A=numpy.matrix([[r4, -r3],[-r3, (r4+rg+r3)]]);#
B=numpy.matrix([[e1],[e2]]);#
X=numpy.dot(numpy.linalg.inv(A),B)
I2=X[1,0]*10**3;#
I1=((e1+(r3*10**-5))/r4);#mA
rp=((e2+(r3*I1)-(r4+rg+r3)*10**-5)/10**-5);#
#results
print 'part b'
print "current is (mA)=",round(I2,3)
print "resistance is (k-ohm)=",round(rp*10**-2,2)
print 'resistance is calculated wrong in the textbook'

part a
current is (A)= 0.02
resistance is (ohm)= 100.0
part b
current is (mA)= 7.078
resistance is (k-ohm)= 2035.32
resistance is calculated wrong in the textbook


## Example 4 - pg 259¶

In :
#pg 259
#Example 4.4: Resistance
#calculate the internal resistance
#given data :
emf=1.01892;# in V
R=1;# in M-ohm
V=1.01874;# in V
#calculations
Ic=V/R;
Vd=emf-V;
Ri=Vd/(Ic*10**-6);
#results
print "internal resistance,Ri(ohm) = ",round(Ri,3)

internal resistance,Ri(ohm) =  176.689


## Example 5 - pg 259¶

In :
#pg 259
#Example 4.5: Resistance
#calculate the resistance
#given data :
l=65;# in cm
V=0.1;# in V
V1=5.5;# in V
R=20;# in ohm
#calculations
E=V*l;
I=V1/R;
Ri=(E-V1)/I;
#results
print "Internal resistance,Ri(ohm) = ",round(Ri,3)

Internal resistance,Ri(ohm) =  3.636


## Example 6 - pg 259¶

In :
#pg 259
#Example 4.6: Resistance
#calculate the resistance
#given
vr=5.;#V
r=10.;#k-ohm
#calculations
x=vr*r*10**3;#
R=x;#
#results
print "resistance is (k-ohm)=",R*10**-3

resistance is (k-ohm)= 50.0


## Example 7 - pg 260¶

In :
#pg 260
#Example 4.7: Length
#calculate the length of the slide wire
#given data :
l=40.;# in cm
r=0.5;# ion ohm
V=1.2;# in V
V1=6;# in V
#calculations
R=r*l/1;# in ohm
I=V/R;
x=V1/(r*I);
#results
print "The length of slide wire (cm) = ",x

The length of slide wire (cm) =  200.0


## Example 8 - pg 260¶

In :
#pg 260
#Example 4.8: design
#calculate the resistance in all cases
#given
vab=1.;#V
i=50.;#mA
n=10.;#
l=100.;#cm
#calculations
vr=2-vab;#V
R=vr/(i*10**-3);#ohm
R1=(vr/10)/(i*10**-3);#ohm
tr1=n*R1;#ohm
r2=2*R1;#
x=R1/l;#
#results
print "resistance R is (ohm)=",R
print "resistance R1 is (ohm)=",R1
print "resistance R2 is (ohm)=",r2
print "resistance per cm of slide wire is (ohm/cm)=",x

resistance R is (ohm)= 20.0
resistance R1 is (ohm)= 2.0
resistance R2 is (ohm)= 4.0
resistance per cm of slide wire is (ohm/cm)= 0.02


## Example 9 - pg 261¶

In :
#pg 261
#Example 4.9.a:resistance
#calculate the resistance, resolution and error
#given
st=15.;#steps
r=5.;#ohm
rsw=5.5;#ohm
vr=1.61;#V
e2=1.61;#V
e1=2.40;#V
trn=11.;#turns
dv=100.;#divisions
ig=0.05;#micro-A
vlt=1.1;#V
ir=50.;#ohm
#calculations
tr=(st*r)+rsw;#ohm
i=vr/tr;#A
rh=(e1-e2)/i;#ohm
slwr=rsw/trn;#ohm
vd=slwr*i;#V
vedv=(1/dv)*vd;#
rs=vedv/5;#
em=((ig*ir));#
#results
print "resistance is (ohm) = ",rh
print "resolution of the instrument is (micro-V) = ",rs*10**6
print "error is (micro-V) = ",em

resistance is (ohm) =  39.5
resolution of the instrument is (micro-V) =  20.0
error is (micro-V) =  2.5


## Example 10 - pg 262¶

In :
#pg 262
#Example 4.10:power dissipated
#calculate the power dissipated and energy stored
#given
import math,cmath
r1=0.6-1j*0.24;#V
r2=0.6+1j*0.4;#V
r3=-0.1-1j*0.4;#V
f=50;#Hx
ir=1000;#ohm
#calculations
i1=r1/ir;#A
pdr=(r1.real*i1.real)+(r1.imag*i1.imag);#W
pdC=(r1.real*i1.real)+(r2.imag*i1.imag);#W
pdc=(r3.real*i1.real)-(r2.imag*i1.imag);#W
imp=(r2/r1)*10**3;#ohm
rc=imp.imag;#ohm
indu=rc/(2*math.pi*f);#H
ersl=(1./2)*(i1.imag**2+i1.real**2)*indu;#joules
ersc=(1./2)*(r3.imag**2+r3.real**2)*C;#
#results
print "power dissipated in the resistor is (mW)=",pdr*10**3
print "power dissipated in the coil is (mW)=",pdC*10**3
print "power dissipated in the capacitor is (mW)=",pdc*10**3
print "energy stored in the coil is (micro-J)=",round(ersl*10**6,2)
print "energy stored in capacitor is (micro-J)=",round(ersc*10**6,3)

power dissipated in the resistor is (mW)= 0.4176
power dissipated in the coil is (mW)= 0.264
power dissipated in the capacitor is (mW)= 0.036
energy stored in the coil is (micro-J)= 0.61
energy stored in capacitor is (micro-J)= 0.42


## Example 11 - pg 263¶

In :
#pg 263
#Example 4.11:measuring range,resulution,working current,setting of the rheostat
#calculate the measuring range,resulution,working current,setting of the rheostat
#given
sd=18.;#steps
v1=0.1;#V
dv=100;#divisions
dr=10;#ohm
wbc=6;#V
#calculations
mr=(sd*v1)+v1;#V
rs=(v1/dv)*(1./2);#mV
cdd=v1/dr;#A
rsv=wbc-mr;#V
sh=rsv/cdd;#ohm
#results
print "measuring range of the potentiometer is (V)=",mr
print "resolution is (mV)=",rs*10**3
print "current through the dial is (mA)=",cdd*10**3
print "setting of the rheostat is (ohm)=",sh

measuring range of the potentiometer is (V)= 1.9
resolution is (mV)= 0.5
current through the dial is (mA)= 10.0
setting of the rheostat is (ohm)= 410.0


## Example 12 - pg 263¶

In :
#pg 263
#Example 4.12:voltage and percentage error
#calculate the voltage and percentage error
#given
st=15;#steps
r1=10;#ohm
v1=0.1;#V
r2=10;#ohm
r3=9.9;#ohm
v2=0.0185;#V
v3=1.0185;#V
n=6;#
vg=0.6525;#
#calculations
acr=(r1*r3)+((r2*v2)/v1);#ohm
I=v3/acr;#
acr1=(n*r3)+(r2*0.0525)/v1;#ohm
tvr=I*acr1;#V
er=((tvr-vg)/tvr)*100;#
#results
print "true value of drop across the resistance is (V)=",round(tvr,4)
print "percentage error is (%)=",round(er,2)

true value of drop across the resistance is (V)= 0.6529
percentage error is (%)= 0.06


## Example 13 - pg 264¶

In :
#pg 264
#Example 4.13:resistance and reactance
#calculate the resistance and reactance
#given
import math,cmath
from math import sqrt,atan,sin
r1=2.;#ohm
r2=9.;#
vm=85.;#V
va=40.;#degree
vm1=90.;#V
va1=45.;#degree
f=50.;#Hz
#calculations
imp=r1+1j*r2;#ohm
mg=sqrt(r1**2+r2**2);#
th=atan(r2/r1) *57.3;#
ccm=vm/mg;#A
cca=va-th;#degree
impm=vm1/ccm;#ohm
impa=va1-cca;#degree
reac=impm*sin(impa/57.3);#ohm
rc=sqrt(impm**2-reac**2);#ohm
ind=reac/(2*math.pi*f);#
#results
print "reactance is (ohm)=",round(rc,2)
print "inductance of the coil is (mH)=",math.floor(ind*10**3)
print 'The answer is a bit different due to rounding off error in textbook'

reactance is (ohm)= 1.28
inductance of the coil is (mH)= 30.0
The answer is a bit different due to rounding off error in textbook


## Example 14 - pg 265¶

In :
#pg 265
#Example 4.14:limit of error,deflection
#calculate the limit of error and deflection of galvanometer
#given
x=17.5;#mm/micro-A
r1=850.;#ohm
v1=2.;#V
r2=80.;#
v3=1.43;#V
v2=0.1;#V
l=50.;#cm
l1=2.;#mm
fr1=22.784;#
#calculations
lr=r1*(1./x);#micro V
i1=v1/r2;#A
r3=v2/i1;#ohm
r4=v3/i1;#ohm
r5=((l1/10.)/l)*r3;#ohm
fr=r4+r5;#ohm
R=(fr*fr1)/r2;#ohm
e=i1*fr;#V
ig=(e-v3)/(r1+R);#A
dg=ig*x*10**6;#mm
#results
print "limit of error in the reading is ",round(lr,1)," micro-V"
print "deflection of the galvanometer is (mm)=",round(dg,1)

limit of error in the reading is  48.6  micro-V
deflection of the galvanometer is (mm)= 8.1


## Example 15 - pg 266¶

In :
#pg 266
#Example 4.15: Current
#calculate the Current
#given data :
V1=4.2;# in V
V2=1.43;# in V
r1=21.0;# in ohm
r2=1.;# in ohm
r3=15.;# in ohm
#calculations
I=V1/r1;# in A
R=V2/I;# in ohm
R1=R+r2;
R2=R-r2;
R3=round(R1*(r1-R1)/r1);
R4=R2*(r1-R2)/r1;
e1=R1*I;
e2=R2*I;
I1=(e1-V2)*10**3/(R3+r3);
I2=(V2-e2)*10**3/(R4+r3);
#results
print "Current in one direction,I1(mA) = ",I1
print "Current in another direction,I2(mA) = ",round(I2,2)

Current in one direction,I1(mA) =  10.0
Current in another direction,I2(mA) =  10.34