Consider a capacitor-charging circuit. Let Q 1 be the charge given to the capacitor in a time interval of 10 ms and Q 2 be the charge given in the next time interval of 10ms. Let 10μC charge be deposited in a time interval t 1 and the next 10 μC charge is deposited in the next time interval t 2 .

Question

Philoid · Accepted Answer

Formula used :

Charge of a capacitor is given by

Charge of a capacitor,

Where

ε is the emf of a battery

C is the capacitance

R is the resistance of a resistor which is in series

T is the time period

charge developed on the capacitor in first interval of 10ms is

charge developed on the capacitor in first interval of 20ms is

Charge developed on the capacitor in the interval 10ms to 20ms is

Compare with

(Here )

The time taking for 10μC to developed on the plates of capacitor is

The time taking for 10μC to developed on the plates of capacitor

Divide (1) by (2)

Take log on both sides

Q₁ is the charge developed on the capacitor in a time interval of 10 ms and Q₂ is the charge developed on the capacitor in the next time interval of 10ms. If a10μC charge be deposited in a time interval t₁ and the next 10 μC charge is deposited in the next time interval t₂. Then Q₁ > Q₂, t₁ < t_2. So option B is correct.

Consider a capacitor-charging circuit. Let Q1 be the charge given to the capacitor in a time interval of 10 ms and Q2 be the charge given in the next time interval of 10ms. Let 10μC charge be deposited in a time interval t1 and the next 10 μC charge is deposited in the next time interval t2.