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Gauss's Law

The charge ac...

Question

The charge across the capacitor in two different $R C$ circuits $1$ and $2$ are plotted as shown in the figure. Identify the correct statement(s) related to the $R_{1}, R_{2}, C_{1}$ and $C_{2}$ of the two $R C$ circuits.

R_{1} > R_{2}

E_{1} = E_{2}

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C_{1} < C_{2}

E_{1} = E_{2}

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R_{1} C_{1} > R_{2} C_{2}

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\frac{R_{1}}{R_{2}} < \frac{C_{2}}{C_{1}}

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Solution

The correct option is D $\frac{R_{1}}{R_{2}} < \frac{C_{2}}{C_{1}}$
The charge on capacitor at any time t is $q = q_{m a x} (1 - e^{- t / C R})$

As the $q_{m a x}$ of the both curve is same so both capacitor will be charged to same charge.

As (2) curve take more time for maximum charging so time constant of curve (2) is greater than (1). i.e, $τ_{2} > τ_{1} \Rightarrow C_{2} R_{2} > C_{1} R_{1}$

$\frac{R_{1}}{R_{2}} < \frac{C_{2}}{C_{1}}$

As $q_{m a x}$ is same for both curve so $C_{1} E_{1} = C_{2} E_{2}$

if $E_{1} = E_{2}, C_{1} = C_{2} \Rightarrow R_{2} > R_{1}$

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The charge across the capacitor in two different RC circuits 1 and 2 are plotted as shown in the figure. Identify the correct statement(s) related to the R1, R2, C1 and C2 of the two RC circuits.

The charge across the capacitor in two different $R C$ circuits $1$ and $2$ are plotted as shown in the figure. Identify the correct statement(s) related to the $R_{1}, R_{2}, C_{1}$ and $C_{2}$ of the two $R C$ circuits.