Question 10

(a) In a metre bridge [Fig. 3.27], the balance point is found to be at 39.5 cm from the end *A*, when the resistor *Y* is of 12.5 **Ω**. Determine the resistance of *X*. Why are the connections between resistors in a Wheatstone or meter bridge made of thick copper strips?

(b) Determine the balance point of the bridge above if *X* and *Y* are interchanged.

(c) What happens if the galvanometer and cell are interchanged at the balance point of the bridge? Would the galvanometer show any current?

Answer

A metre bridge with resistors* X* and *Y* is represented in the given figure.

(a) Balance point from end A, *l*_{1} = 39.5 cm

Resistance of the resistor *Y* = 12.5 **Ω**

Condition for the balance is given as,

Therefore, the resistance of resistor *X* is 8.2 **Ω**.

The connection between resistors in a Wheatstone or metre bridge is made of thick copper strips to minimize the resistance, which is not taken into consideration in the bridge formula.

(b) If *X* and *Y* are interchanged, then *l*_{1} and 100 - *l*_{1} get interchanged.

The balance point of the bridge will be 100 - *l*_{1} from A.

100 - *l*_{1} = 100 - 39.5 = 60.5 cm

Therefore, the balance point is 60.5 cm from A

(c) When the galvanometer and cell are interchanged at the balance point of the bridge, the galvanometer will show no deflection. Hence, no current would flow through the galvanometer.

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