At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V?[Take : ln 5 = 1.6, ln 3 = 1.1]

Engineering

Physics

Parallel Plate Capacitor

Circuit Analysis Having Capacitor Only

RC Circuit

Question

At time t = 0, a battery of 10 V is connected across points A and B in the given circuit. If the capacitors have no charge initially, at what time (in seconds) does the voltage across them become 4 V?

[Take : ln 5 = 1.6, ln 3 = 1.1]

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4 = Q = eV (1 – e^–t/RC)

4 = 10

$\frac{2}{5} = 1 - e^{- t / RC}$

$e^{- t / RC} = \frac{3}{5}$

$\frac{t}{RC} = 1 .6 - 1 .1 = 0 .5$

t = 1 × 10^–6 × 4 × 10^–6 × 0.5 = 2 sec.