Question

$\orange\implies$$\mathfrak{Question}$
On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10 cm.

The
resistance of their series combination is 1 kilo-ohm.
How much was the resistance on the left slot before

interchanging the resistances?​

Answer 1

Answer:550Ω

Explanation:

Formula Used:

R1l=R2(100−l)
R
1
l
=
R
2
(
100
−
l
)

Here R1
R
1
is the resistance on the left side of the galvanometer, R2
R
2
is the resistance of the galvanometer, l
l
is the distance of the galvanometer from the left end and 100−l
100
−
l
is the distance of the galvanometer from the right end.

Complete step by step answer:
In the question the total resistance is given as 1kΩ
1
k
Ω
i.e. 1000Ω
1000
Ω
. So,
⇒R1+R2=1000
⇒
R
1
+
R
2
=
1000

⇒R2=1000−R1
⇒
R
2
=
1000
−
R
1

Here R1
R
1
is the resistance on the left side of the galvanometer and R2
R
2
is the resistance of the galvanometer in the initial condition.
The given question can be better understood using a figure.

This is the initial condition of the Wheatstone bridge as given in the question. As it is in balance condition, we can use the formula of equal gradients on both sides.
⇒R1l=1000−R1(100−l)
⇒
R
1
l
=
1000
−
R
1
(
100
−
l
)

Let this be equation 1.
It’s given that if we interchange the resistance on the right and resistance on the left, the balancing point shifts 10cm
10
c
m
to the left.
lnew=l−10
l
n
e
w
=
l
−
10
and
lnew−100=l+10−100
l
n
e
w
−
100
=
l
+
10
−
100

Here lnew
l
n
e
w
is the distance of the galvanometer from the left end for the new position and lnew−100
l
n
e
w
−
100
is the distance of the galvanometer from the right end for the new position.

As this condition is also a balanced condition, we can use the formulae of balanced Wheatstone bridge. So,
⇒1000−R1lnew=R1(100−lnew)
⇒
1000
−
R
1
l
n
e
w
=
R
1
(
100
−
l
n
e
w
)

⇒1000−R1l−10=R1(100−(l+10))
⇒
1000
−
R
1
l
−
10
=
R
1
(
100
−
(
l
+
10
)
)

Let this be equation 2.
By solving equation 1 and 2 we will get the value of l=55cm
l
=
55
c
m

By using this value of ll
in equation 1 we will get the value of R1=550Ω

R1=550Ω
.

Answer 2

Answer:

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