Question

FIGURE Q28.13 shows the voltage as a function of time of a capacitor as it is discharged (separately) through three different resistors. Rank in order, from largest to smallest, the values of the resistances $R_1\mathrm{to}{R}_3$

Short answer

Order of the values of the resistances is${\mathit{R}}_{\mathbf{2}}\mathbf{>}\mathbf{}{\mathit{R}}_{\mathbf{3}}\mathbf{>}\mathbf{}{\mathit{R}}_{\mathbf{1}}$

Step-by-step solution

Given information and formula used 

Given :

Theory used :

Resistance directly affects the time required to charge a capacitor. As resistance increases, it takes more time to charge a capacitor. The amount of time for the capacitor to become fully charged in a $RC$circuit depends on the values of the capacitor and resistor in the circuit

Ranking in order, from largest to smallest, the values of the resistances.

A bigger resistance results in a larger time constant $t=RC$, which means the voltage decreases more slowly.

It makes no difference how big the initial voltage is. Because the $R_2$curve decays the slowest, $R_2$is the greatest, and the $R_1$curve decays the fastest, $R_1$is the smallest. That is,

${\mathit{R}}_{\mathbf{2}}\mathbf{>}\mathbf{}{\mathit{R}}_{\mathbf{3}}\mathbf{>}\mathbf{}{\mathit{R}}_{\mathbf{1}}$