A Wheatstone bride is almost balanced with point `C` grounded. Calculate (a) the potential of point `B` (b) the potential of point `D` (c) If a galvanometer is connected between B and D, what is the direction of current through it ? (d) For what value of the resistance `BC` would the bridge be in balanced state ?

Options

A. 33V, 32V and `22 Omega`
B. 30V, 23V and `11 Omega`
C. 32V, 33V and `10 Omega`
D. 15V, 20 V and `20 Omega`

Answer

A

Explanation

Current through `DAC=(48)/(5+11)=(48)/(16)=3 A`
`rArr " " V_(AC)=11xx3=33 V`
and `V_(A)-V_(C )=33V`
as `V_(C )=0 rArr V_(A)=33 V`
Similarly, current through `DBC = (48)/(10+20)=(48)/(30)=1.6`
`rArr " " V_(BC)=20xx1.6 = 32 V`
or `V_(B)-V_(C )=32 V`
as `V_(C )=0 rArr V_(A)=33 V`
Similarly, current through `DBC = (48)/(10+20)=(48)/(30)=1.6`
`rArr " " V_(BC)=20xx1.6=32 V`
or `V_(B)-V_(C )=32 V`
as `V_(C )=0rArr V_(B)=32 V`
For balanced bridge, `(R_(BC))/(R_(BD))=(R_(AC))/(R_(DA))rArr (R_(BC))/(10)=(11)/(5)rArr R_(BC)=22 Omega`