(A) The relationship between current $I$ and charge $q$ is given by $I = \frac{dq}{dt}$.Therefore,the charge $dq$ is $dq = I \, dt = (3t^2 + 2t + 5) \

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(A) The relationship between current $I$ and charge $q$ is given by $I = \frac{dq}{dt}$.Therefore,the charge $dq$ is $dq = I \, dt = (3t^2 + 2t + 5) \, dt$.To find the total charge $q$ passing through the cross-section from $t = 0$ to $t = 2$ seconds,we integrate the expression:$q = \int_{0}^{2} (3t^2 + 2t + 5) \, dt$$q = [t^3 + t^2 + 5t]_{0}^{2}$Substituting the limits:$q = (2^3 + 2^2 + 5(2)) - (0^3 + 0^2 + 5(0))$$q = (8 + 4 + 10) - 0 = 22 \, C$.Thus,the total charge is $22 \, C$.

Class 12 Physics Current Electricity Electric Current

Medium

The current flowing through a wire varies with time according to the formula $I = 3t^2 + 2t + 5$. The total charge passing through a cross-section of the wire in the interval from $t = 0$ to $t = 2$ seconds is ........... $C$.

A
$22$
B
$20$
C
$18$
D
$5$

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If an electron revolves in a circular path of radius $0.5 \times 10^{-10} \ m$ at a frequency of $5 \times 10^{15} \ Hz$,the electric current in the circle is .................. $mA$. (Charge of an electron $= 1.6 \times 10^{-19} \ C$)

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In an electrolyte,$3.2 \times 10^{18}$ bivalent positive ions drift to the right per second,while $3.6 \times 10^{18}$ monovalent negative ions drift to the left per second. Then the current is:

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In a conducting region, $10^{19}$ electrons and $10^{19}$ protons move to the left, while $10^{19}$ $\alpha$-particles move to the right per second. The resulting electric current is $(e = 1.6 \times 10^{-19} \text{ C})$

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The current flowing through a wire varies with time according to the formula $I = 3t^2 + 2t + 5$. The total charge passing through a cross-section of the wire in the interval from $t = 0$ to $t = 2$ seconds is ........... $C$.

Similar Questions

$A$ current of $5\,A$ flows through a resistance of $10\, \Omega$ for $4$ minutes. The total charge in Coulombs and the number of electrons passing through any cross-section of the resistor in this time are, respectively:

The current passing through a copper voltameter is $3.2 \ A$. The number of copper ions $(Cu^{2+})$ deposited at the cathode per minute is:

If an electron revolves in a circular path of radius $0.5 \times 10^{-10} \ m$ at a frequency of $5 \times 10^{15} \ Hz$,the electric current in the circle is .................. $mA$. (Charge of an electron $= 1.6 \times 10^{-19} \ C$)

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In a conducting region, $10^{19}$ electrons and $10^{19}$ protons move to the left, while $10^{19}$ $\alpha$-particles move to the right per second. The resulting electric current is $(e = 1.6 \times 10^{-19} \text{ C})$

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