Time constant of a capacitor and capacitance are 5s and $100 n F$ . It is charged from zero by a cell of emf $10 V$ through a resistor. The charge on it after 3 s is.

4.5 \times 10^{- 6} C

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9 \times 10^{- 6} C

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4.5 \times 10^{- 7} C

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9 \times 10^{- 7} C

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Solution

The correct option is C $4.5 \times 10^{- 7} C$
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 sec,
$q = 100 \times 10^{- 9} \times 10 (1 - e^{- \frac{3}{5}})$
$q = 10^{- 6} (0.451)$
$q = 4.51 \times 10^{- 7} C$

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Time constant of a capacitor and capacitance are 5s and 100 nF. It is charged from zero by a cell of emf 10 V through a resistor. The charge on it after 3 s is.

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

Time constant of a capacitor and capacitance are 5s and $100 n F$ . It is charged from zero by a cell of emf $10 V$ through a resistor. The charge on it after 3 s is.

The correct option is C $4.5 \times 10^{- 7} C$
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 sec,
$q = 100 \times 10^{- 9} \times 10 (1 - e^{- \frac{3}{5}})$
$q = 10^{- 6} (0.451)$
$q = 4.51 \times 10^{- 7} C$