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An unknown resistance X is connected in the left gap and a known resistance R in the right gap of a meter bridge. The balance point is obtained at 55 cm from the left end of the wire. When R is increased by 5 Ω , the balance point shifts by 5 cm. The value of X is
- a)5 Ω
- b)1 Ω
- c)27.5 Ω
- d)11/9 Ω
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
An unknown resistance X is connected in the left gap and a known resis...
Solution:
Given, unknown resistance X is connected in the left gap and a known resistance R in the right gap of a meter bridge.
Balance point is obtained at 55cm from the left end of the wire.
When R is increased by 5, the balance point shifts by 5cm.
Let the length of the wire be L.
Then, the resistance in left gap = X and resistance in right gap = R.
Let the balance length of wire be l.
Then, X/R = (L-l)/l
=> X = R(L-l)/l
When R is increased by 5, the balance point shifts by 5cm.
Let the new balance length be l1 and new resistance be R1.
Then, X/R1 = (L-l1)/l1
=> X = R1(L-l1)/l1
Also, given (L-l1)/l1 - (L-l)/l = 5/L
=> (l1-l)/(l1l) = 5/L
=> (l1-l)L = 5l1l
=> l1-l = 5L/l
Substitute this value in the equation X = R1(L-l1)/l1
=> X = R1((L-(l+5L/l))/l+5L/l)
=> X = R1(L^2/l(l+5L))
Substitute the value of X in the equation X = R(L-l)/l
=> R(L-l)/l = R1(L^2/l(l+5L))
=> R/R1 = l+5L/l
Substitute the given balance length l = 55 cm and R1 = R+5
=> R/R+5 = 55+5L/55
=> 55R = (R+5)(55+5L)
=> 55R = 55L+5R+275
=> 50R = 55L+275
Substitute the value of R/R+5 = 55+5L/55 in the equation X = R(L-l)/l
=> X = (55+5L)(L-55)/55
=> X = L^2 - 55L
Substitute the value of R/R+5 = 55+5L/55 in the equation 50R = 55L+275
=> 50(55+5L/55) = 55L+275
=> L = 27.5
Substitute the value of L in X = L^2 - 55L
=> X = 27.5^2 - 55(27.5)
=> X = 756.25 - 1512.5
=> X = -756.25
Therefore, the value of X is -756.25 which is not in the given options.
Hence, there may be an error in the question or solution provided.
Given, unknown resistance X is connected in the left gap and a known resistance R in the right gap of a meter bridge.
Balance point is obtained at 55cm from the left end of the wire.
When R is increased by 5, the balance point shifts by 5cm.
Let the length of the wire be L.
Then, the resistance in left gap = X and resistance in right gap = R.
Let the balance length of wire be l.
Then, X/R = (L-l)/l
=> X = R(L-l)/l
When R is increased by 5, the balance point shifts by 5cm.
Let the new balance length be l1 and new resistance be R1.
Then, X/R1 = (L-l1)/l1
=> X = R1(L-l1)/l1
Also, given (L-l1)/l1 - (L-l)/l = 5/L
=> (l1-l)/(l1l) = 5/L
=> (l1-l)L = 5l1l
=> l1-l = 5L/l
Substitute this value in the equation X = R1(L-l1)/l1
=> X = R1((L-(l+5L/l))/l+5L/l)
=> X = R1(L^2/l(l+5L))
Substitute the value of X in the equation X = R(L-l)/l
=> R(L-l)/l = R1(L^2/l(l+5L))
=> R/R1 = l+5L/l
Substitute the given balance length l = 55 cm and R1 = R+5
=> R/R+5 = 55+5L/55
=> 55R = (R+5)(55+5L)
=> 55R = 55L+5R+275
=> 50R = 55L+275
Substitute the value of R/R+5 = 55+5L/55 in the equation X = R(L-l)/l
=> X = (55+5L)(L-55)/55
=> X = L^2 - 55L
Substitute the value of R/R+5 = 55+5L/55 in the equation 50R = 55L+275
=> 50(55+5L/55) = 55L+275
=> L = 27.5
Substitute the value of L in X = L^2 - 55L
=> X = 27.5^2 - 55(27.5)
=> X = 756.25 - 1512.5
=> X = -756.25
Therefore, the value of X is -756.25 which is not in the given options.
Hence, there may be an error in the question or solution provided.
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Community Answer
An unknown resistance X is connected in the left gap and a known resis...
X/R= 55/45
X/R+5 = 50/50
solving we get R= 22.5
and X= 27.5
X/R+5 = 50/50
solving we get R= 22.5
and X= 27.5
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Question Description
An unknown resistance X is connected in the left gap and a known resistance R in the right gap of a meter bridge. The balance point is obtained at 55 cm from the left end of the wire. When R is increased by 5 , the balance point shifts by 5 cm. The value of X isa)5 b)1 c)27.5 d)11/9 Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An unknown resistance X is connected in the left gap and a known resistance R in the right gap of a meter bridge. The balance point is obtained at 55 cm from the left end of the wire. When R is increased by 5 , the balance point shifts by 5 cm. The value of X isa)5 b)1 c)27.5 d)11/9 Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An unknown resistance X is connected in the left gap and a known resistance R in the right gap of a meter bridge. The balance point is obtained at 55 cm from the left end of the wire. When R is increased by 5 , the balance point shifts by 5 cm. The value of X isa)5 b)1 c)27.5 d)11/9 Correct answer is option 'C'. Can you explain this answer?.
An unknown resistance X is connected in the left gap and a known resistance R in the right gap of a meter bridge. The balance point is obtained at 55 cm from the left end of the wire. When R is increased by 5 , the balance point shifts by 5 cm. The value of X isa)5 b)1 c)27.5 d)11/9 Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An unknown resistance X is connected in the left gap and a known resistance R in the right gap of a meter bridge. The balance point is obtained at 55 cm from the left end of the wire. When R is increased by 5 , the balance point shifts by 5 cm. The value of X isa)5 b)1 c)27.5 d)11/9 Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An unknown resistance X is connected in the left gap and a known resistance R in the right gap of a meter bridge. The balance point is obtained at 55 cm from the left end of the wire. When R is increased by 5 , the balance point shifts by 5 cm. The value of X isa)5 b)1 c)27.5 d)11/9 Correct answer is option 'C'. Can you explain this answer?.
Solutions for An unknown resistance X is connected in the left gap and a known resistance R in the right gap of a meter bridge. The balance point is obtained at 55 cm from the left end of the wire. When R is increased by 5 , the balance point shifts by 5 cm. The value of X isa)5 b)1 c)27.5 d)11/9 Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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