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A Wheatstone bridge circuit is constructed with three resistors R1 = 100 \Omega, R2 = 150 \Omega, and R3 = 300 \Omega, and an unknown resistor Rx. A galvanometer is connected across the bridge’s null points. If the bridge is balanced when Rx = 200 \Omega, calculate the resistance Rx when the bridge is balanced again after replacing R3 with R4 = 250 \Omega.

Option: 1

475 \Omega


Option: 2

375 \Omega


Option: 3

575 \Omega


Option: 4

675 \Omega


Answers (1)

best_answer

Given:

Resistor values:

R1 = 100 \Omega, R2 = 150 \Omega, R3 = 300 \Omega, Rx = 200 \Omega

Replaced resistor value: R4 = 250 \Omega 
The Wheatstone bridge equation for balance is given by:

                \frac{R_{1}}{R_{2}} = \frac{R_{3}}{R_{z}}

Step 1: Calculate the value of Rx when the bridge is initially balanced:

                \frac{R_{1}}{R_{2}} = \frac{R_{3}}{R_{z}}

                \frac{100 \Omega}{150 \Omega} = \frac{300 \Omega}{R_{z}}

R_{z} = \frac{300 \Omega * 150 \Omega}{100 \Omega} = 450 \Omega

Step 2: Calculate the value of Rz when the bridge is balanced with R4 replacing R3:

                    \frac{R_{1}}{R_{2}} = \frac{R_{4}}{R_{z}}

                    \frac{100 \Omega}{150 \Omega} = \frac{250 \Omega}{R_{z}}

R_{z} = \frac{250 \Omega * 150 \Omega}{100 \Omega} = 375 \Omega

The resistance Rz when the bridge is balanced again after replacing R3 with R4 is 375 \Omega.

 

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Sayak

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