A capacitor is discharged through a resistance in RC circuit. The variation of loge i with time t is shown by a dotted line in the figure, where i is the discharging current. If the resistance in the circuit be doubled, the variation of loge i with time t would be best represented by the line

Question

A capacitor is discharged through a resistance in RC circuit. The variation of loge i with time t is shown by a dotted line in the figure, where i is the discharging current. If the resistance in the circuit be doubled, the variation of loge i with time t would be best represented by the line (A) P (B) Q (C) R (D) S

Tardigrade Admin · Accepted Answer

In R-C circuit i = (E/R) e-t/RC ∴ loge i = (-t/RC) + loge (E/R) Value of R is double, the slope of curve will increase. At t =0, for increased value of resistance, current will be minimum.

P

Q

R

S

In R−C circuit i=RE​e−t/RC ∴loge​i=RC−t​+loge​RE​ Value of R is double, the slope of curve will increase. At t=0, for increased value of resistance, current will be minimum.

In $R - C$ circuit $i = \frac{E}{R} e^{- t / RC}$
$∴ l o g_{e} i = \frac{- t}{RC} + l o g_{e} \frac{E}{R}$
Value of $R$ is double, the slope of curve will increase.
At $t = 0$ , for increased value of resistance, current will be minimum.