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  •   is the ideal voltmeter in the figure. Resistance of the resistor shown in R. initially the

\mathrm{V_c}  is the ideal voltmeter in the figure. Resistance of the resistor shown in R. initially the switch is in position 2 when charging of the capacitor starts. Initially the capacitor was uncharged. The witch in circuit shifts automatically from 2 to 1 when \mathrm{V_C>2 \mathrm{~V} / 3} and goes back to 2 from 1 when \mathrm{V_C<V / 3} . The ideal voltmeter reads voltage across capacitor as plotted. What is the period T of the wave form in terms of R and C ?

Option: 1

3RC In 3 


Option: 2

2RC In 2 


Option: 3

(RC/2) In 2 


Option: 4

None of these


Answers (1)

best_answer

\mathrm{t_1}  is the time of capacitor to discharge from \mathrm{2 \mathrm{~V} / 3 ~to ~\mathrm{V} / 3}  For this, \mathrm{\frac{V}{3}=\frac{2 V}{3} e_1^{-t / \tau} \Rightarrow t_1=\tau \ln 2=R C}   in 2

\mathrm{t_2}  is time for charging of capacitor from  \mathrm{\mathrm{V} / 3~ to ~2 \mathrm{~V} / 3}
So   \mathrm{\int_{V C / 3}^{2 V C / 3} \frac{d q}{V C-q}=\int_0^{t_2} \frac{d t}{R C} \Rightarrow t_2=R C~ In~ 2}
\mathrm{T=t_1+t_2=2 R C \ln 2}

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Divya Prakash Singh

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