Q. 16

# Consider a capaci A. Q_{1} > Q_{2}, t_{1} > t_{2} B. Q_{1} > Q_{2}, t_{1} < t_{2}

C. Q_{1} < Q_{2}, t_{1} > t_{2} D. Q_{1} < Q_{2}, t_{1} < t_{2}

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

Q_{1} is the charge developed on the capacitor in a time interval of 10 ms and Q_{2} is the charge developed on the capacitor in the next time interval of 10ms. If a10μC charge be deposited in a time interval t_{1} and the next 10 μC charge is deposited in the next time interval t_{2}. Then Q_{1} > Q_{2}, t_{1} < t_{2.} So option B is correct.

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