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  • In a precision meter bridge experiment, a uniform wire of length 100 cm is used. A standard resistor R1 with a value of 150 is connected in series with an unknown resistor R. The bridge

In a precision meter bridge experiment, a uniform wire of length 100 cm is used. A standard resistor R1 with a value of 150 is connected in series with an unknown resistor R. The bridge circuit is set up so that the balance point is found at a distance of 75 cm from one end of the wire. The wire has a negligible resistance and a uniform cross-sectional area. The resistances in the circuit are temperature-compensated. Determine the value of the unknown resistor R to the nearest hundredth of an ohm.

Option: 1

100.00


Option: 2

125.00


Option: 3

133.33


Option: 4

140.00


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_1}{L_2}

Where R1 is the known resistor value, 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.

\text { Given that } R_1=150 \Omega, L_1=75 \mathrm{~cm} \text {, and } L_2=100-75=25 \mathrm{~cm} \text { : }\frac{150}{R}=\frac{75}{25}=3

Solving for R:

R=\frac{150}{3}=50 \Omega

However, this value of R corresponds to the resistance of R1, which is incorrect. The bridge is only balanced when R balances R1, so we must invert the ratio:

\begin{gathered} \frac{R_1}{R}=\frac{L_2}{L_1} \\ \frac{150}{R}=\frac{25}{75}=\frac{1}{3} \end{gathered}

Solving for R:

R = 150 × 3 = 450 ?

The actual value of R is 450 ?, which corresponds to the standard resistor R1. This indicates that the balance point should be at the center of the wire, and the unknown resistor R should also be 450 ?.

Therefore, the correct answer is: B) 450.00

Posted by

Shailly goel

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