# An Unknown Resistance R1 is Connected in Series

By Varadi Hema|Updated : July 29th, 2022

An unknown resistance R1​ is connected in series with a resistance of 10Ω. This combination is connected to one gap of a meter bridge while a resistance R2​ is connected to the other gap. The balance point is at 50 cm. Now when the 10Ω resistance is removed, the balance point shifts to 40 cm. The value of R1​ is (in ohms):
A. 60 ohms
B. 20 ohms
C. 40 ohms
D. 10 ohms

## An unknown resistance R1​ is connected in series with a resistance of 10Ω. This combination is connected to one gap of a meter bridge while a resistance R2​ is connected to the other gap. The balance point is at 50 cm. Now when the 10Ω resistance is removed, the balance point shifts to 40 cm. The value of R1​ is (in ohms):20 ohms.

Solution:

Given an unknown resistance, R1​ is connected in series with a resistance of 10Ω .

The balance point l1=50 cm

it is a meter bridge,

so l1+l2=100 cm

l2=100-l1=50 cm

(R1+10)/R2=l1/l2=l1/(100-l1)

(R1+10)/R2=50/(100-50)

R1+10=R2________(1)

When the 10-ohm resistor is removed, The balance point l1=40 cm.

l2=100-l1=100-40=60

R1/R2=l1/l2=40/60

R1=2/3R2 _________(2)

By solving equations (1) &(2)

R1=20 Ohms