In the circuit shown in figure, reading of voltmeter is `V_1` when only `S_1` is closed, reading of voltmeter is `V_2` when only `S_2` is closed, and reading of voltmeter is `V_3` when both `S_1 and S_2` are closed. Then .

Options

A. `V_(3)gtV_(2)gtV_(1)`
B. `V_(2)gtV_(1)gtV_(3)`
C. `V_(3)gtV_(1)gtV_(2)`
D. `V_(1)gtV_(2)gtV_(3)`

Explanation

`omega` about `I.A.O.R = (v_(0))/(l sin theta)`
EMF across `OQ = (1)/(2)(omega)Bl^(2)cos^(2)theta`
EMF across `OP=(1)/(2)(omega)Bl^(2)sin^(2)theta`
EMF across `PQ=(1)/(2)Bomegal^(2)(cos^(2)theta-sin^(2)theta)`
`=(1)/(2)B(v_(0))/(lsintheta)l^(2)(cos^(2)theta-sin^(2)theta)`
`(Bv_(0)l)/(2((1)/(2)))((3)/(4)-(1)/(4))=(Bv_(0)l)/(2)`