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  • In a highly precise meter bridge experiment, a resistance R is connected in the gap of a meter-long wire. A standard resistor 1R with a value of 100 is connected in series with R. The fol

In a highly precise meter bridge experiment, a resistance R is connected in the gap of a meter-long wire. A standard resistor 1R with a value of 100 is connected in series with R.

The following additional data is given:

• The balance point is found at a distance of 40 cm from one end of the wire.

• The wire has a uniform cross-sectional area, and its resistance is negligible.

• The resistances in the bridge circuit are temperature-compensated.

Determine the value of the unknown resistance R to the nearest hundredth of an ohm.

 

Option: 1

50.00


Option: 2

72.73


Option: 3

81.82


Option: 4

90.91


Answers (1)

best_answer

The meter bridge experiment uses the principle of a balanced Wheatstone bridge. In a balanced bridge:

\frac{R}{1 R}=\frac{L 2}{L 1}

Where L1 is the length of the wire on one side of the gap (from one end to the balance point) and L2 is the length on the other side. Given that 1R = 100 ?, L1 = 40 cm, and L2 = 60 cm:

\frac{100 \Omega}{R}=\frac{60 \mathrm{~cm}}{40 \mathrm{~cm}}=\frac{3}{2}

Solving for R:

R=\frac{2}{3} \times 100 \Omega=150 \Omega

However, this value of R corresponds to the resistance of 1R, which is incorrect. The bridge is only balanced when R balances 1R, so we must invert the ratio:

\frac{R}{1 R}=\frac{2}{3}

Solving for R:

R=\frac{2}{3} \times 100 \Omega=150 \Omega

The actual value of R is 150 ?, which corresponds to the standard resistor 1R. This indicates that the balance point should be at the center of the wire, and the resistor R should also be 100 ?.

Therefore, the correct answer is C) 81.82 ?.

 

Posted by

Sanket Gandhi

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