A wheatstone bridge is assembled with resistance in arm AB, BC and AD

1.	A wheatstone bridge is assembled with resistance in arm AB, BC and AD as 5 ohm, 15 ohm, 3 ohm respectively. what resistance should be inserted in arm CD to make it balanced????
Answer» Given : Resistance in arm AB = 5Ω Resistance in arm BC = 15Ω Resistance in arm AD = 3Ω To Find : What resistance should be inserted in arm CD to make it balanced! Solution : ❖ In the balanced Wheatstone bridge, the resistance in arm BD is INEFFECTIVE. The EQUIVALENT resistance of the balanced Wheatstone bridge between the POINT A and C is $\dag\:\underline{\boxed{\bf{\gray{R_{eq}=\dfrac{(P+Q)(R+S)}{P+Q+R+S}}}}}$ For a balanced Wheatstone bridge; $\dag\:\underline{\boxed{\bf{\pink{\dfrac{P}{Q}=\dfrac{R}{S}}}}}$ By substituting the given VALUES; $\sf:\implies\:\dfrac{P}{Q}=\dfrac{R}{S}$ $\sf:\implies\:\dfrac{5}{15}=\dfrac{3}{S}$ $\sf:\implies\:S=\dfrac{3\times 15}{5}$ $\sf:\implies\:S=3\times 3$ $:\implies\:\underline{\boxed{\bf{\green{S=9\:\Omega}}}}$

A wheatstone bridge is assembled with resistance in arm AB, BC and AD as 5 ohm, 15 ohm, 3 ohm respectively. what resistance should be inserted in arm CD to make it balanced????

Answer»

Given :

Resistance in arm AB = 5Ω

Resistance in arm BC = 15Ω

Resistance in arm AD = 3Ω

To Find :

What resistance should be inserted in arm CD to make it balanced!

Solution :

❖ In the balanced Wheatstone bridge, the resistance in arm BD is INEFFECTIVE. The EQUIVALENT resistance of the balanced Wheatstone bridge between the POINT A and C is

$\dag\:\underline{\boxed{\bf{\gray{R_{eq}=\dfrac{(P+Q)(R+S)}{P+Q+R+S}}}}}$