# Chapter 7 Electrical Measurements¶

## Example 7.1 Page no 229¶

In [33]:
#Given
R1=2
R2=3
R3=5
E1=6
E2=4

#Calculation
import math
A=np.array([[7,5],[5,8]])
b=np.array([6,4])
z=np.linalg.solve(A,b)
Z=z[0]
Z1=z[1]
A1=Z+Z1

#Result
print"Current through R1 is", round(Z,3),"A"
print"Current through R2 is", round(Z1,3),"A"
print"Current through R3 is",round(A1,2),"A"

Current through R1 is 0.903 A
Current through R2 is -0.065 A
Current through R3 is 0.84 A


## Example 7.2 Page no 229¶

In [42]:
#Given
E1=1.5                    #V
E2=2.0                    #V
r1=1                      #ohm
r2=2                      #ohm
R=5                       #ohm

#Calculation
import math
A=np.array([[6,5],[5,7]])
B=np.array([1.5,2])
Z=np.linalg.solve(A,B)
Z1=Z[0]
Z2=Z[1]
A1=(Z1+Z2)*R

#Result
print"Current through R1 is", round(Z1,4),"A"
print"Current through R2 is",round(Z2,4),"A"
print"Current through R3 is",round(A1,4),"A"

Current through R1 is 0.0294 A
Current through R2 is 0.2647 A
Current through R3 is 1.4706 A


## Example 7.3 Page no 230¶

In [26]:
#Given
E1=2                        #V
E2=1                        #V
E3=4                        #V
r1=4                        #ohm
r2=3                        #ohm
r3=2                        #ohm

#Calculation
import math
A=np.array([[1,1,1],[4,-3,0],[0,3,-2]])
A1=np.array([0,1,-3])
Z=np.linalg.solve(A,A1)
Z1=Z[0]
Z2=Z[1]
Z3=Z[2]

#Result
print"Current through R1 is", round(Z1,2),"A"
print"Current through R2 is",round(Z2,2),"A"
print"Current through R3 is",round(Z3,2),"A"

Current through R1 is -0.15 A
Current through R2 is -0.54 A
Current through R3 is 0.69 A


## Example 7.4 Page no 230¶

In [25]:
#Given
R1=5                   #ohm
R3=2
R=10

#Calculation
import math
A=np.array([[9,5],[10,19]])
A1=np.array([1,1])
Z=np.linalg.solve(A,A1)
Z1=Z[0]
Z2=Z[1]
I=(Z1+Z2)*R

#Result
print"Potential difference across the resistor is", round(I,4),"V"

Potential difference across the resistor is 1.0744 V


## Example 7.5 Page no 230¶

In [51]:
#Given
A=10                              #ohm
B=5                               #ohm
S=2

#Calculation
import math
A=np.array([[25,-10],[5,5]])
B=np.array([9,7])
Z=np.linalg.solve(A,B)
Z1=Z[1]*10

#Result
print"Equivalent resistance is", round(Z1,0),"ohm"

Equivalent resistance is 7.0 ohm


## Example 7.6 Page no 231¶

In [8]:
#Given
P=15                              #ohm
Q=12.0
R=10.0
S=4

#Calculation
R1=S*(P/Q)
X=1/(1/R1-1/R)

#Result
print"The resistance to be connectedin parallel is",X,"ohm"

The resistance to be connectedin parallel is 10.0 ohm


## Example 7.7 Page no 231¶

In [41]:
#Given
P=4.0
Q=4.0
R=4.0
X=4.0

#Calculation
R1=P+Q
R2=R+X
R3=1/(1/R1+1/R2)
I=P/R3
I1=I/2

#Result
print"(i) Equivalent resistance is",R3,"ohm"
print"(ii) The magnitudes of current is",I1,"A"

(i) Equivalent resistance is 4.0 ohm
(ii) The magnitudes of current is 0.5 A


## Example 7.8 Page no 232¶

In [59]:
#Given
a=4
b=3
c=2.0
E=6                   #v

#Calculation
X=(a*b)/c
R1=a+c
R2=b+R1
R=((R1*R2)/(R1+R2))+2.4
I=E/R

#Result
print"Current drawn by the circuit is", I,"A"
print"Unknown resistance is",R,"ohm"

Current drawn by the circuit is 1.0 A
Unknown resistance is 6.0 ohm


## Example 7.9 Page no 232¶

In [68]:
#Given
a=1.5
b=5
c=6

#Calculation
I1=a/(b+c)
I2=I1/10.0
I=I1+I2

#Result
print"Current in the arms is", round(I1,4),"A and",round(I2,4),"A"
print"Current in the cell is",I,"A"

Current in the arms is 0.1364 A and 0.0136 A
Current in the cell is 0.15 A


## Example 7.10 Page no 233¶

In [71]:
#Given
X=10
P=3
Q=2.0

#Calculation
R=X*P/Q
L=1/R

#Result
print"Length is",round(L,3),"m"

Length is 0.067 m


## Example 7.11 Page no 233¶

In [76]:
#Given
r=6                        #ohm
l=1/3.0
r1=2/3.0

#Calculation
R1=r/((2.0*(r1/l))-1)
R2=2*R1

#Result
print"Resistance of two wires is", R1,"ohm and",R2,"ohm"

Resistance of two wires is 2.0 ohm and 4.0 ohm


## Example 7.12 Page no 233¶

In [83]:
#Given
P=1.2                        #ohm
Q=0.8
R=2
E=4                              #V

#Calculation
X=(R*P)/Q
R1=X+R
R2=P+Q
R11=R1*R2/(R1+R2)
I=E/R11

#Result
print"Unknown resistance is", X,"ohm"
print"Current drawn is",I,"A"

Unknown resistance is 3.0 ohm
Current drawn is 2.8 A


## Example 7.13 Page no 233¶

In [87]:
#Given
R=20.0                     #ohm
V=10**-3                  #V/m
l=10**4                   #mm
V1=10**-2                     #V

#Calculation
I=V1/R
R1=(2/I)-R

#Result
print"Value of resistance is", R1,"ohm"

Value of resistance is 3980.0 ohm


## Example 7.14 Page no 233¶

In [93]:
#Given
l1=65                    #cm
l2=60.0
a=0.1

#Calculation
E1=((a*l1)/l2)/((l1/l2)-1)
E2=E1-a

#Result
print"E.m.f of cell is", E1,"V and",E2,"V"

E.m.f of cell is 1.3 V and 1.2 V


## Example 7.15 Page no 234¶

In [138]:
#Given
S=9.5                 #ohm
I1=76.3               #cm
l2=64.8

#Calculation
r=((I1/I2)-1)*S

#Result
print"Internal resistance is",round(r*10**-3,1),"ohm"

Internal resistance is 53.1 ohm


## Example 7.16 Page no 234¶

In [111]:
#Given
E=10*10**-3
r=10
l=40                  #cm

#Calculation
R=10*l/100.0
R1=(R*2/E)-10

#Result
print"External resistance is", R1,"ohm"

External resistance is 790.0 ohm


## Example 7.17 Page no 234¶

In [116]:
#Given
R1=10*10**3
E=12

#Calculation
R=R1/((E/2.0)-1)

#Result
print"(a) Resistance is",R*10**-3,"K ohm"
print"(b) When current flows through a resistor,its temperature increases due toheat produced across it."

(a) Resistance is 2.0 K ohm
(b) When current flows through a resistor,its temperature increases due toheat produced across it.


## Example 7.18 Page no 235¶

In [120]:
#Given
a=3.0
b=6.0

#Caculation
E=(1/a)+(1/b)+1+(1/a)

#Result
print"Equivalent resistance is",round(E,2),"r"

Equivalent resistance is 1.83 r


## Example 7.22 Page no 237¶

In [125]:
#Given
a=5
b=10

#Calculation
import math
A=np.array([[7,1],[1,5]])
A1=np.array([2,2])
B=np.linalg.solve(A,A1)
B1=B[0]
B2=B[1]
E=(a*B2)+(B1*b)

#Result
print"Equivalent resistance is", round(E,2),"ohm"

Equivalent resistance is 4.12 ohm


## Example 7.23 Page no 238¶

In [135]:
#Given
R=12.5
l=39.5

#Calculation
X=(R*(100-l))/l
L=X/(X+R)

#Result
print"(a) Resistance is",round(X,2),"W"
print"(b) Balance point of bridge is", L*10**2,"cm"
print"(c) The galvanometer will not show any current."

(a) Resistance is 19.15 W
(b) Balance point of bridge is 60.5 cm
(c) The galvanometer will not show any current.