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Byju's Answer

Standard XII

Physics

Charge Behaviour

Plot a graph ...

Question

Plot a graph of the potential difference $V_{2}$ versus $t$ and determine the instantaneous value of $V_{2}$

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Solution

To find time constant of the circuit we will have to short circuit the battery and find resistance across capacitor. In that case $R_{1}$ and $R_{2}$ are in parallel and they are in series with $R_{3}$ .
$∴ R_{n e t} = 3 + \frac{4 \times 6}{4 + 6} = 5.4 M Ω$
$∴ τ_{C} = C R_{n e t} = (10 \times 10^{- 6}) (5.4 \times 10^{6})$
$= 54 s$
$∴ V_{2} = 6 + (10.8 - 6) (1 - e^{- t / C})$
$= 6 + 4.8 (1 - e^{t / 54})$
Here $V_{2}$ is in kV and t is second.

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Plot a graph of the potential difference V2 versus t and determine the instantaneous value of V2

Plot a graph of the potential difference $V_{2}$ versus $t$ and determine the instantaneous value of $V_{2}$