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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) ? 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` |
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Answer» Correct Answer - C 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`. |
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