The electric current through a wire varies with time as I = I₀ + β t, where I₀ = 20 A and β = 3 A/s. The amount of electric charge crossed through a section of the wire in 20 s is: (a) 80 C (b) 800 C (c) 1000 C (d) 1600 C

Answer: (c). q = ∫₀²⁰ (I₀ + β t) dt = I₀ t + β t²2 q = 20 × 20 + (3 × 400)/(2) = 400 + 600 q = 1000 C So the answer is (c) 1000 C.

The electric current through a wire varies with time as I = I₀ + β t… | JEE Main 2024 (29 Jan, Shift 1)

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Electric Current, Drift Velocity & Current Density

The electric current through a wire varies with time as $I = I_0 + \beta t$ , where $I_0 = 20\text{ A}$ and $\beta = 3\text{ A/s}$ . The amount of electric charge crossed through a section of the wire in $20\text{ s}$ is:

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Answer: (c)

$q = \int_0^{20} (I_0 + \beta t)\,dt = I_0 t + \dfrac{\beta t^{2}}{2}$
$q = 20 \times 20 + \dfrac{3 \times 400}{2} = 400 + 600$
$q = 1000\text{ C}$
So the answer is (c) 1000 C.

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