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A series combination of 0.1 \mathrm{M} \Omega  resistor and a 10 \mu \mathrm{F} capacitor is connected across a 1.5 \mathrm{~V} source of negligible resistance. The time required for the capacitor to get charged up to  0.75 \mathrm{~V} is approximately (in seconds)

Option: 1

\infty


Option: 2

\log _e 2


Option: 3

\log _{10} 2


Option: 4

zero


Answers (1)

best_answer

 


q=C E\left[1-e^{-t / R C}\right]
or 0.75 \times 10^{-5}=10^{-5} \times 1.5\left[1-e^{-\frac{t}{10^5 \times 10^{-5}}}\right]
or \frac{1}{2}=\left[1-e^{-t}\right] \ or \ e^{-t}=\frac{1}{2}
Taking log on both sides, we get
-t=-\ln 2 \\ or \ t=0.693 s.

Posted by

seema garhwal

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