In the circuit shown below, all the three voltmeters are identical and have very high resistance (but not `oo` ). Each resistor has the same resistance. The voltage of the ideal battery shown is 9V. Find the reading of voltmeter `V_3` (in volts).

Options

A. 3
B. 6
C. 2
D. 9

Answer

C

Explanation

Taking potential at A to be zero, potential at B = 3 V and potentiaI at B. = 3V and potential at C = 6V

Let `V_D` be potential of point D then sum of currents reaching point D is zero
`(V_B- V_D)/( R_(V_2)) + (V_B.- V_D)/( R_(V_1))+ ((V_C- V_D))/( R_(V_3))=0`
`[ R_(V_2) = R_(V_1)= R_(V_3)= R.]`
`rArr (3-V_(D))/(R.)+ (3- V_(D))/( R.) + (6- V_(D))/( R.) = 0`
`rArr 12-3 V_(D) =0 , V_(D) = 4` volts
`therefore` reading of `V_3=2` volts.