The electric current in a conductor varies wi | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The relationship between current $I$ and charge $Q$ is given by $I = \frac{dQ}{dt}$,which implies $dQ = I \ dt$.To find the total charge $Q$ passi

Vedclass · Accepted Answer

$24$

Vedclass · Answer

(B) The relationship between current $I$ and charge $Q$ is given by $I = \frac{dQ}{dt}$,which implies $dQ = I \ dt$.To find the total charge $Q$ passing through the cross-section between time $t_1 = 2 \ s$ and $t_2 = 3 \ s$,we integrate the current with respect to time:$Q = \int_{2}^{3} I \ dt = \int_{2}^{3} (2t + 3t^2) \ dt$Performing the integration:$Q = [t^2 + t^3]_{2}^{3}$$Q = (3^2 + 3^3) - (2^2 + 2^3)$$Q = (9 + 27) - (4 + 8)$$Q = 36 - 12 = 24 \ C$.Thus,the total charge passed is $24 \ C$.

The electric current in a conductor varies with time $t$ as $I = 2t + 3t^2$,where $I$ is in amperes and $t$ is in seconds. Find the total charge $Q$ (in $C$) that passes through the cross-section of the conductor from $t = 2 \ s$ to $t = 3 \ s$.

Similar Questions

In a region,$10^{19}$ $\alpha$-particles and $10^{19}$ protons per second move to the left,while $10^{19}$ electrons move to the right per second. The current is

Define the $SI$ unit of electric charge in terms of the Ampere.

Current passing through a wire as a function of time is given as $I(t) = 0.02t + 0.01 \ A$. The charge that will flow through the wire from $t = 1 \ s$ to $t = 2 \ s$ is: (in $C$)

The current through a wire depends on time as $i = (2+3t)\, mA$. The charge crossing through a section of the wire in $1\, min$ is .............. $C$.

$A$ steady current flows in a metallic conductor of non-uniform cross-section. The quantity/quantities constant along the length of the conductor is/are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module