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Displacement Current

A 4μ F capa...

Question

A $4 μ F$ capacitor, a resistance of $2.5 M Ω$ is in series with $12 V$ battery. Find the time after which the potential difference across the capacitor is $3$ times the potential difference across the resistor. [Given: $l n (b) = 0.693]$

13.86 s

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6.93 s

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7 s

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14 s

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Solution

The correct option is A $13.86 s$
Here, $V_{C} = 3 V_{R} = 3 (V_{0} - V_{C})$ where $V_{0} = 12 V$ , applied voltage.
$V_{C} = \frac{3}{4} V_{0}$
$V_{0} (1 - e^{- t / R C}) = \frac{3}{4} V_{0}$
$e^{- t / R C} = \frac{1}{4}$
$e^{t / R C} = 4$
Take $l n$ both sides, $t / R C = l n 4$
$t = 2 R C l n 2 = 2 \times 2.5 \times 10^{6} \times 4 \times 10^{- 6} l n 2 = 13.86 s$

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A 4μF capacitor, a resistance of 2.5MΩ is in series with 12V battery. Find the time after which the potential difference across the capacitor is 3 times the potential difference across the resistor. [Given: ln(b)=0.693]

The correct option is A 13.86sHere, VC=3VR=3(V0−VC) where V0=12V, applied voltage.VC=34V0V0(1−e−t/RC)=34V0e−t/RC=14et/RC=4Take ln both sides, t/RC=ln4t=2RCln2=2×2.5×106×4×10−6ln2=13.86s

A $4 μ F$ capacitor, a resistance of $2.5 M Ω$ is in series with $12 V$ battery. Find the time after which the potential difference across the capacitor is $3$ times the potential difference across the resistor. [Given: $l n (b) = 0.693]$