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) gt V_(2) gt V_(1)`
B. `V_(2) gt V_(1) gt V_(3)`
C. `V_(3) gt V_(1) gt V_(2)`
D. `V_(1) gt V_(2) gt V_(3)`

Answer

B

Explanation

(b) In series , potential difference `prop R`
When only `S_(1)` is closed, `V_(1) = (3)/(4) E = 0.75 E`
When only `S_(2)` is closed, `V_(2) = (6)/(7) E = 0.86 E`
and when both `S_(1)` and `S_(2)` are closed combined resistance of `6R` and `3R` is `2R`.
`V_(3) = ((2)/(3)) E = 0.67 E`
Hence `V_(2) gt V_(1) gt V_(3)`.