# Chapter 6 Electrical measurements¶

## Example 6.1 Page no 332¶

In [20]:
#Given
a=4
b=2.0
c=8
d=5
e=3.0

#Calculation
I1=((a*c)+(b*e))/((b*c)+(d*e))
I2=(a-(2*I1))/e
V=(I1-I2)*5

#Result
print"(i) Current through each battery is", round(I1,2),"A and",round(I2,2),"A"
print"(ii) Terminal voltage is",round(V,2),"V"

(i) Current through each battery is 1.23 A and 0.52 A
(ii) Terminal voltage is 3.55 V


## Example 6.4 Page no 334¶

In [33]:
#Given
a=10
b=5.0
c=9.0
d=19.0

#Calculation
I2=(a-c)/((b*a)-(d*c))
I1=(1-(5*I2))/c
I=I1+I2
pd=I*10

#Result
print"Current through each cell is", round(I,2),"A"
print"Potential difference across 10 ohm wire is",round(pd,3),"V"

Current through each cell is 0.11 A
Potential difference across 10 ohm wire is 1.074 V


## Example 6.6 Page no 335¶

In [47]:
#Given
a=-3
b=4.0
c=3

#Calculation
I1=a/(b+(c**2))
I2=-1-c*I1
I3=-(I1+I2)

#Result
print"Current through each cell is", round(I1,2),"A ,",round(I2,2),"A and",round(I3,2),"A"

Current through each cell is -0.23 A , -0.31 A and 0.54 A


## Example 6.7 Page no 336¶

In [51]:
#Given
a=15
b=4
c=12.0
d=10

#Calculation
R=(a*b)/c
X=(d*R)/(d-R)

#Result
print"The value of resistance is", X,"ohm"

The value of resistance is 10.0 ohm


## Example 6.8 Page no 336¶

In [59]:
#Given
R1=4                  #ohm
R2=3                 #ohm
R3=2.0
R11=2.4               #ohm
E=6

#Calculation
X=(R1*R2)/R3
R4=R2+X
R5=R1+R3
Rt=((R4*R5)/(R4+R5))+R11
I=E/Rt

#Result
print"the value of unknown resistance is", X,"ohm"
print"The current drawn by the circuit is",I,"A"

the value of unknown resistance is 6.0 ohm
The current drawn by the circuit is 1.0 A


## Example 6.9 Page no 337¶

In [70]:
#Given
a=10
b=7.0
c=5
d=4
e=8.0

#Calculation
I1=(a+a)/(b+1)
I3=(c+(4*I1))/e
I2=(-a+(6*I3)+I1)/2.0

#Result
print"Current I1=",I1,"A \nI2=",I2,"A \nI3=",I3,"A"

Current I1= 2.5 A
I2= 1.875 A
I3= 1.875 A


## Example 6.11 Page no 338¶

In [74]:
#Given
a=28
b=5.0
c=2

#Calculation
Rak=a/(b*c)

#Result
print"Total resistance from one end of vacant edge to other end is", Rak,"ohm"

Total resistance from one end of vacant edge to other end is 2.8 ohm


## Example 6.12 Page no 345¶

In [78]:
#Given
R=10
l2=68.5
l1=58.3

#Calculation
X=R*(l2/l1)

#Result
print"Value of X is", round(X,1),"ohm"

Value of X is 11.7 ohm


## Example 6.13 Page no 346¶

In [85]:
#Given
R=2                   #ohm
R1=2.4                 #ohm
V=4                    #V
E=1.5

#Calculation
R11=R+R1
I=V/R11
Vab=I*R
K=Vab
l=E/K

#Result
print"Length for zero galvanometer deflection is", l,"m"

Length for zero galvanometer deflection is 0.825 m


## Example 6.15 Page no 347¶

In [95]:
#Given
l1=33.7
l2=51.9

#Calculation
S1=l1/(100-l1)
s11=l2/(100-l2)
s=((s11*12)/S1)-12
R=s*S1

#Result
print"Value of R is", round(R,2),"ohm \nValue of S is",round(s,1),"ohm"

Value of R is 6.85 ohm
Value of S is 13.5 ohm


## Example 6.16 Page no 347¶

In [103]:
#Given
a=0.4
b=0.6
lab=10

#Calculation
K=a/b
Vab=K*lab

#Result
print"(i) Potentila gradient along AB is",round(K,2),"V/m"
print "(ii) P.D between point A and B is",round(Vab,2),"V"

(i) Potentila gradient along AB is 0.67 V/m
(ii) P.D between point A and B is 6.67 V


## Example 6.17 Page no 348¶

In [111]:
#Given
R1=990                        #ohm
R=10.0                        #ohm
E=2
l=1000                            #mm
l1=400                            #mm

#Calculation
Rt=R1+R
I=E/Rt
pd=I*R
K=pd/l
pd1=K*l1

#Result
print"e.m.f. generated by the thermocouple is", pd1,"V"

e.m.f. generated by the thermocouple is 0.008 V


## Example 6.18 Page no 348¶

In [124]:
#Given
AB=600              #cm
AC=500.0               #cm
l=40*10**-3           #A
E=2
r=10

#Calculation
R=2*AB/(AC*l)
K=2/AC
AC1=AC-r
pd=K*AC1
Iv=(E-pd)/r
R1=pd/Iv

#Result
print"(i) The resistance of the whole wire is", R,"ohm"
print"(ii) Reading of voltmeter is", pd,"V"
print"(iii) Resistance of the voltmeter is",R1,"ohm"

(i) The resistance of the whole wire is 60.0 ohm
(ii) Reading of voltmeter is 1.96 V
(iii) Resistance of the voltmeter is 490.0 ohm


## Example 6.20 Page no 350¶

In [130]:
#Given
a=6
b=2

#Calculation
R1=a/((b*b)-1)
R2=b*R1

#Result
print"Resistance R1 is", R1,"ohm \nR2 is",R2,"Ohm"

Resistance R1 is 2 ohm
R2 is 4 Ohm


## Example 6.21 Page no 350¶

In [134]:
#Given
R=20                       #ohm
L=10                       #m
pd=10**-3                  #V/m
V=10**-2                   #Volts

#Calculation
I=V/R
R11=(2/I)-R

#Result
print"The value of resistance is", R11,"ohm"

The value of resistance is 3980.0 ohm