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Relation between P, V, T, Gamma in Adiabatic Proceses

Three identic...

Question

Three identical capacitors A, B and C are charged to the same potential and them made to discharge through three resistances $R_{A}, R_{B}$ and $R_{C}$ , where $R_{A} > R_{B} > R_{C}$ . Their potential difference (V) are plotted against time $t$ , giving the curves 1, 2 and 3. Find the correlations between A, B, C and 1, 2, 3

A

1 \to A

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B

2 \to B

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C

1 \to C

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D

3 \to A

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Solution

The correct options are
B $2 \to B$
C $1 \to C$
D $3 \to A$
The expression of potential in a function of time t during discharging resistor R is
$V (t) = V_{0} (1 - e^{- t / C R})$
As $R_{A} > R_{B} > R_{C}$ , So curve for $R_{A}$ has less slope than curve $R_{B}$ and it has less slope than the curve for $R_{C}$ .
Thus, $3 \to A, 2 \to B$ and $1 \to C$

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