The electric current through a wire varies with time as I=I 0 +β t. where I 0 =20 A and β=3 A / s . The amount of electric charge crossed through a section of the wire in 20 s is :

Physics · Current Electricity

JEE Main 2024 — 29 January, Shift 1 — Question 31

The electric current through a wire varies with time as $I=I_{0}+\beta$ t. where $I_{0}=20 \mathrm{~A}$ and $\beta=3 \mathrm{~A} / \mathrm{s}$ . The amount of electric charge crossed through a section of the wire in 20 s is :

Option A:
80 C
Option B:
1000 C
Correct
Option C:
800 C
Option D:
1600 C

Answer: B

Step-by-step solution

Given that Current $I=I_{0}+\beta t$

$\mathrm{I}_{0}=20 \mathrm{~A}$

$\beta=3 \mathrm{~A} / \mathrm{s}$

$\mathrm{I}=20+3 \mathrm{t}$

$\frac{d q}{d t}=20+3 t$

$\int_{0}^{q} d q=\int_{0}^{20}(20+3 t) d t$

$\mathrm{q}=\int_{0}^{20} 20 \mathrm{dt}+\int_{0}^{20} 3 t d t$

$q=\left[20 t+\frac{3 \mathrm{t}^{2}}{2}\right]_{0}^{20}=1000 \mathrm{C}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 29 January, Shift 1
Subject: Physics
Chapter: Current Electricity
Topic: Current in Conductors, Drift Speed, Resistivity and Relaxation Time

Answer: B

Step-by-step solution

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