The circuit shown in the figure consists of a charged capacitor of capacity $3 \mu \mathrm{~F}$ and a charge of $30 \mu \mathrm{C}$. At time $\mathrm{t}=0$, when the key is closed, the value of current flowing through the $5 \mathrm{M} \Omega$ resistor is 'x' $\mu \mathrm{A}$. The value of 'x' to the nearest integer is ______

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Current Electricity

The circuit shown in the figure consists of a charged capacitor of capacity

3 μ F

and a charge of

30 μ C

. At time

t = 0

, when the key is closed, the value of current flowing through the

5 M Ω

resistor is 'x'

μ A

.
The value of 'x' to the nearest integer is ______

Answer: 2

The potential difference across the capacitor at the instant the key is closed is

V = \frac{q}{C} = \frac{30 μ C}{3 μ F} = 10 V

The capacitor, the

5 M Ω

resistor and the key form a single loop, and at

t = 0

the capacitor still carries its full charge, so the whole of this

10

V drives current through the resistor:

I_{0} = \frac{V}{R} = \frac{10}{5 \times 1 0 ^{6}} = 2 \times 1 0^{- 6} A

The current through the

5 M Ω

resistor at

t = 0

2 μ A

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Integer answer