A voltmeter of variable ranges 3V, 15V, 150 V is to designed by connecting resistances `R_(1), R_(2), R_(3)` in series with a galvanometer of resistance `G=20Omega`, as shown in the figure. The galvanometer gives full pass through its coil. Then, the resistances `R_(1), R_(2) and R_(3)` (in kilo ohms) should be, respectively

Options

A. `4sqrt(6)`
B. `2sqrt(6)`
C. `3sqrt(6)`
D. `6sqrt(6)`

Answer

A

Explanation

Suppose `Q_(2)Q_(3)` intersects `R_(2)R_(3)` at R. Then, R divides `Q_(2)Q_(3)` internally in the ratio of radii of circles `C_(2)` and `C_(3)` respectively. But, `C_(2) and C_(3)` are of the same radius. So, R is the mid-point of `Q_(2)Q_(3)` as well as that of `R_(2)R_(3)`. The coordinates of R are (0, 3).
In right triangle `Q_(2)R_(2)R`, we obtain
`Q_(2)R^(2)=Q_(2)R_(2)^(2) + R R_(2)^(2)`
`rArr 6^(2)=(2sqrt(3))^(2)+R R_(2)^(2) rArr R R_(2) = sqrt(36-12)=2sqrt(6)`
Hence, `R_(2)R_(3)=2R R_(2)=4sqrt(6)`.