Question

At what value should the
variable resistor be set such that the bridge is balanced? If the source voltage is 30 V
find the value of the output voltage across XY, when the bridge is balanced.​

Answer 1

Given :

Four resistors are connected as shown in figure across a battery of 30V.

• P = 1360 Ω
• R = 300 Ω
• S = 4400 Ω

To Find :

Value of variable resistor Q and voltage across XY when bridge is balanced.

Solution :

❒ The wheatstone bridge is most sensitive when the resistance in the four arms are of the same order.

• Wheatstone bridge method is not suitable for the measurement of very low and very high resistances.

In the balanced Wheatstone bridge, the resistance in arm BD is ineffective.

For a balanced Wheatstone bridge,

$\sf:\implies\:\dfrac{P}{Q}=\dfrac{R}{S}$

By substituting the given values,

$\sf:\implies\:\dfrac{1360}{Q}=\dfrac{300}{4400}$

$\sf:\implies\:Q=\dfrac{1360\times 44}{3}$

$\sf:\implies\:Q=\dfrac{59840}{3}$

$\bf:\implies\:Q=19946.67\:\Omega=19.94\:k\Omega$

No current flow in branch BD when Wheatstone bridge is in balanced condition.

Hence in balanced condition voltage across XY will be zero.

Answer 2

Four resistors are connected as shown in figure across a battery of 30V.

• P = 1360 Ω
• R = 300 Ω
• S = 4400 Ω

To Find :

Value of variable resistor Q and voltage across XY when bridge is balanced.

Solution :

❒ The wheatstone bridge is most sensitive when the resistance in the four arms are of the same order.

Wheatstone bridge method is not suitable for the measurement of very low and very high resistances.

In the balanced Wheatstone bridge, the resistance in arm BD is ineffective.

For a balanced Wheatstone bridge,

⟹ $QP = SR$

By substituting the given values,

⟹ $Q1360 = 4400300$

⟹$Q= 31360×44$

⟹$Q= 359840$

⟹$Q=19946.67Ømega=19.94kØmega$

No current flow in branch BD when Wheatstone bridge is in balanced condition.

Hence in balanced condition voltage across XY will be zero