In the given circuit, the value of m is varying. The correct statements about the circuit are

Options

A. The condition for maximum current flowing from x is m = 2.
B. The maximum current is `V//sqrt2r . `
C. The condition for maximum current flowing from x is `m = sqrt2`.
D. The maximum current is `3V//2r`.

Answer

B, C

Explanation

b., c. `R_(q) = m/2 + r/m`
`I = V/((mr)/2 + r/m)`

For maximum current `(mr)/2 + r/m` should be minimum
But `((mr)/2 + r/m) = (sqrt((mr)/2)- sqrt(r/m))^2) + 2(mr)/2 r/m`
`=(sqrt((mr)/2) - sqrt(r/m))^2 + r^2`
For minimum value `sqrt((mr)/2) = sqrt(r/m)`m = sqrt(2)`
And maximum current from (i),
`I = V/((sqrt2r)/2+ r/(sqrt2)) = V/sqrt2r`.