A source of emf `E=10 V` and having negligible internal resistance is connected to a variable resistance. The resistance varies as shown in figure. The total charge that has passed through the resistor `R` during the time interval from `t_1` or `t_2` is

Options

A. `40 log_4`
B. `30 log_e3`
C. `20 log_e2`
D. `10 log_e2`

Answer

D

Explanation

Let `R=at+b`
At `= t = 10s, R=20 Omega`
`:. 20=10a+b` …………..i
at `t = 3a+b`…………ii
Solving these two equations, we get
`a=1.0 Omega//s`
and `b=10 Omega`
`:. R=(t+10)`
`i=E/R=10/(t+10)`
`/_\q=int_10^30 dt`
`=int_10^30((10)/(t+10))dt`
`=10 log_e(2)`