Electric charge passing through a resistor changes with time t as Q = at - ` bt^(2)` . Then total heat produce in resistor R = ....

Options

A. `(a)/(2b)`
B. `(2b)/(a)`
C. `(a^(2))/(2b^(2))`
D. `(R(a^(3)))/(6(b))`

Answer

A

Explanation

`(a)/(2b)`
Q = at - `bt^(2) `
I = `(dQ)/(dt ) = (d)/(dt) [ at - bt^(2) ]`
I = a - 2 bt
For maximum current is should be `(dQ)/(dt) ` = 0 For resistance R.
`therefore 0 =at - 2bt " " therefore t = (a)/(2b)`