Question

Four resistances 5Ω ,10Ω ,15Ω and an unknown XΩ are connected in series so as to form Wheatstone's network. Determine the unknown resistance X, if the network is balanced with these numerical values of resistances.
(Ans : X = 7.5 Ω)

Answer 1

Um.........
Tough question. The figure should look like this.,.........as given.
The figure shows how a wheatstone bridge looks. But here the question is saying that they are connected in series. Also there should be 5 resistances. There are given only four. Where did you get this question? .
If no one else answers, search Google.
Hope this helps.

Answer 2

Unknown resistance X is 7.5 ohm.

We know that a wheatstone is electrical circuit used to measure unknown resistance by balancing the two legs of bridge with one leg having unknown component.

At the point of balance both voltage and current between midpoints are zero .Hence I1=I2 and I3=Ix of unknown resistance.

So we have for a balanced wheatstone bridge

V1/V2=V3/Vx

So V=IR  hence I1R1/I2R2=I3R3/IxRx

So R1/R2=R3/Rx

R1=5 R2=10 so R1/R2=5/10=1/2

solving we get R4=7.5 ohm