14. MAGNETIC EFFECT OF ELECTRIC CURRENT
1.
A rectangular coil in a moving
galvanometer has 50 turns each of length
5 cm and breadth 3 cm, which is
suspended in a radial magentic field of
0.050 Wb/m 2 . The twist constant of
suspension is 1.5 × 10 –9 Nm/deg.
Calculate the current through the coil
which will deflect it through 300.
Given :
n
=
50
C
=
1.5 × 10–9 Nm/deg
B
=
0.05 Wb/m2
θ
=
300
A
=
l×b
=
5×3
=
15 cm2
=
15 × 10–4 m2
To Find :
I
= ?
Formula :
Formula :
=
 Ig

 I – Ig


G


S
=
 Ig

 I – Ig


G


S
=
 5 × 10 –3

–3
 5 – 5 × 10
S
Solution :
∴
∴

 × 40

=
0.04 Ω
S
=
0.04 Ω
A shunt of 0.04 Ω is to be connected in
parallel with galvanometer (convert if in
to am meter of range 0 – 5 A).
Calculate the value of resistance needed
to
convert a moving coil galanometer of
I
=
60 Ω into an ammeter of range 5 A which
Solution :
gives full scale deflection for a current
of 50 mA and into voltmeter of range
cθ
I
=
0 – 50 V.
nAB
Given :
G
=
60 Ω
1.5 × 10 –9 × 30
I
=
V
=
50 V
–4
50 × 15 × 10 × 0.05
I
=
5A
∴
I
=
1.2 × 10–5 A
Ig
=
50 mA
= 50 × 10–3 A
–2
=
5 × 10 A
2.
A galvanometer with a coil of resistance To Find :
40 ohm gives a full scale deflection for
i)
Rs
=
?
a current of 5 mA. How will you convert Formula :
it into an ammeter of range 0–5 A ?
V
Given :
i)
Rs
=
–G
I
G
=
40 Ω
g
Ig
=
5 mA
GIg
=
5 × 10–3 A
ii)
S
=
I
=
5A
I – Ig
To Find :
S
=
?
cθ
nAB
3.
Magnetic Effect of Electric Current
MAHESH TUTORIALS SCIENCE
.. 88
Solution :
Rs
∴
∴
=
Rs
=
Rs
Rs
=
=
S
=
S
=
V
–G
Ig
∴
(G + X) + S
=
50
∴
(16 + X + 0.04)
=
∴
∴
∴
(16 + X + 0.04)
X
X
=
=
=
5 × 10–2
1000 – 60
940 Ω
– 60
GIg
10
× 0.04
2 × 10–2
20
20 – 16.04
3.96 Ω
5.
I – Ig
60 × 0.05
5 – 0.05
3
4.95
S
=
0.6061 Ω
A resistance of 0.6061 Ω in parallel and
940 Ω in series is connected to M.C.G.
=
∴
∴
I
S
Ig
A resistance of 3 ohm is connected in
parallel to a galvanometer of resistance
297 ohm. Find the fraction of current
passing through galvanometer.
Given :
S
=
3 Ω
G
=
297 Ω
To Find :
Ig
I
Formula :
4.
A galvanometer has a resistance of 16 Ω
I gG
and gives a full scale deflection when a Solution :
current of 20 mA is passed through it.
I gG
The only shunt resistance available is
G
0.04 Ω which is not appropriate to ∴
+1
S
convert galvanometer into an ammeter.
How much resistance should be
G+S
connected in series with coil of
∴
S
galvanometer so that the range of
ammeter is 10 A ?
Solution :
Ig
∴
Let ‘X’ be the resistance connected in
I
series with galvanometer.
Since S is not sufficient for I = 10 A
Ig
∴
G = 16 Ω,
=
?
=
(I – Ig)S
=
(I – Ig)S
=
I
Ig
=
I
Ig
=
S
G+S
=
=
3
300
 3

× 100 
= 
 300

=
0.01 or 1 %
I
Ig G = 16 Ω
G
X
∴
Ig
3
297 + 3
I
6.
S = 0.04 Ω
∴
From the figure,
Ig
I
=
S
(G + X) + S
Magnetic Effect of Electric Current
The
combined
resistance
of
galvanometer of resistance 1000 ohm
and its shunt is 25 ohm. Calculate the
value of shunt.
MAHESH TUTORIALS SCIENCE
Given :
G
=
Req =
To Find :
S
=
Formula :
Solution :
Current sensitivity of MCG
1000 Ω
25 Ω
Si
=
?
=
1
1
+
G
S
1
R eq
=
1
1
+
G
S
1
S
=
1
1
–
G
R eq
∴
S
=
∴
S
=
1
R eq
.. 89
∴
Si
=
Si
=
nAB
c
50 × 12 × 10–4 × 0.025
15 × 10 –10
106 deg/A
Solution :
=
∴
S
=
=
G – R eq
R eq G
R eq G
G – R eq
25 × 1000
1000 – 25
25 × 1000
975
25.64 Ω
7.
A rectangular coil of moving coil
galvanometer contains 50 turns each
having area 12 cm2. It is suspended in
radial magentic field of induction
0.025 Wb/m2 by a fibre of twist constant
15 × 10–10 Nm/deg. Calculate the sensitvity
of a moving coil galvanometer.
Given :
n
=
50
A
=
12 cm2
=
12 × 10–4 m2
B
=
0.025 Wb/m2
c
=
15 × 10–10 Nm/deg
To Find :
Si
=
?
Formula :
Si
=
nAB
c
Magnetic Effect of Electric Current