The time constant of a capacitor is 5sec. If the capacitance is C=100nF and it is charged from zero by a cell of EMF 10V through a resistor. What is the charge on it after 3 seconds?

4 \times 10^{- 7} C

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4.5 \times 10^{- 7} C

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5 \times 10^{- 7} C

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5.5 \times 10^{- 7} C

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Solution

The correct option is B $4.5 \times 10^{- 7} C$
Use the equation,
$q = C E (1 - e^{- \frac{t}{R C}})$
We know that time constant, $τ = R C = 5 s$
So,
At t=3,
$q = 100 \times 10^{- 9} \times 10 (1 - e^{- \frac{3}{5}})$
$q = 10^{- 6} (0.451)$
$q = 4.51 \times 10^{- 7} C$

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The time constant of a capacitor is 5sec. If the capacitance is C=100nF and it is charged from zero by a cell of EMF 10V through a resistor. What is the charge on it after 3 seconds?

The correct option is B 4.5×10−7CUse the equation, q=CE(1−e−tRC) We know that time constant, τ=RC=5s So, At t=3, q=100×10−9×10(1−e−35) q=10−6(0.451) q=4.51×10−7C

The correct option is B $4.5 \times 10^{- 7} C$
Use the equation,
$q = C E (1 - e^{- \frac{t}{R C}})$
We know that time constant, $τ = R C = 5 s$
So,
At t=3,
$q = 100 \times 10^{- 9} \times 10 (1 - e^{- \frac{3}{5}})$
$q = 10^{- 6} (0.451)$
$q = 4.51 \times 10^{- 7} C$