A battery of emf 2 V and initial resistance `1 Omega` is
connected across terminals A and B of the circuit shown
in figure
.

Options

A. Thermal power generated in the external circuit will be maximum possible when `R = 16//25 Omega`.
B. Maximum possible thermal power generated in the external circuit is equal to 4 W.
C. Ratio of current through `3Omega` to that through `8Omega` is independent of R.
D. None of above.

Answer

A, C

Explanation

a., b., c.
In the simplified circuit, the circuit is a balanced Wheatstone
bridge and a branch of `20//29 Omega and R ` is paralllel with this
balanced bridge for maximum power.

`r = R_(external)`
` 1 = 1/(1/(3+6) + 1/(20//29+R) + 1/(4+8))`
or `R = 16/25 Omega`
Maximum power developed in the external circuit is
`P_(max) = i^2R = (2/(1+1))^2 xx 1 = 1W`
Current through the upper branch
`i_1 = i[((20/29+R)(4+8))/(9+(20/29 + R)+12)]`
`i_2 = i[((20/29+R)(3+6))/(9+(20/29 + R)+12)]`
Therefore, `i_1//i_2` is independent of R.