A graph between current and time during charging of a capacitor by a battery in series with a resistor is shown. The graphs are drawn for two circutis. `R_1, R_2, C_1, C_2` and `V_1, V_2` are the values of resistance, capacitance and `EMF` of the cell in the two circuits. If only two parameters (out of resistance, capacitance, `EMF`) are different in the two circuits. What may be the correct options (s) ?

Options

A. `V_1=V_2,R_1gtR_2,C_1gtC_2`
B. `V_1gtV_2,R_1gtR_2,C_1=C_2`
C. `V_1ltV_2,R_1ltR_2,C_1=C_2`
D. `V_1ltV_2,R_1=R_2,C_1,C_2`

Answer

C

Explanation

Changing current is given by
`i=i_0e^(-t//tau_C)`
or `i=V/Re^(-t//CR)`
If we have take log on both sides, we have
`ln(i)=ln(V/R)-(1/(CR))t`
Hence ln(i) versus `t` graph is a straight line with slope `(-1/(CR))` and intercept `+ln(V/R)` .
Intercepts are same, but `|slope_i|gt|slope|_2`.