Three identical capacitor are given a charge Q each and they are allowed to discharge through resistor R₁, R₂ and R₃. Their charges as a function of time are shown in graph below. The smallest of the three resistance is:

Question

Aicharya · Accepted Answer

As the capacitors are discharging,

For discharging R-C circuit,

$Q = C V e^{- t / R C}$

For any time $t$ , $Q_{3} > Q_{2} > Q_{1}$

$\Rightarrow C V e^{- t / R_{3} C} > C V e^{- t / R_{2} C} > C V e^{- t / R_{1} C}$

$\Rightarrow \frac{1}{e^{- t / R_{3} C}} > \frac{1}{e^{- t / R_{2} C}} > \frac{1}{e^{- t / R_{1} C}}$

$\Rightarrow e^{t / R_{3} C} < e^{t / R_{2} C} < e^{t / R_{1} C}$

$\Rightarrow \frac{t}{R_{3} C} < \frac{t}{R_{2} C} < \frac{t}{R_{1} C}$

$\Rightarrow R_{3} > R_{2} > R_{1}$

So the smallest resistance is $R_{1}$ .

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Three identical capacitor are given a charge Q each and they are allowed to discharge through resistor R 1 ,…

Solution