The current in a conductor varies with time t | 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 $Q$ flow

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 $Q$ flowing between $t = 2 \, s$ and $t = 3 \, s$,we integrate the current with respect to time:$Q = \int_{2}^{3} I \, dt = \int_{2}^{3} (2t + 3t^2) \, dt$$Q = \left[ \frac{2t^2}{2} + \frac{3t^3}{3} \right]_{2}^{3} = \left[ t^2 + t^3 \right]_{2}^{3}$$Q = (3^2 + 3^3) - (2^2 + 2^3)$$Q = (9 + 27) - (4 + 8)$$Q = 36 - 12 = 24 \, C$.

The current in a conductor varies with time $t$ as $I = 2t + 3t^2$,where $I$ is in ampere and $t$ is in seconds. The electric charge flowing through a section of the conductor during $t = 2 \, s$ to $t = 3 \, s$ is ............. $C$.

Similar Questions

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 $(e = 1.6 \times 10^{-19} \text{ C})$

The charge flowing in a conductor varies with time as $Q = at - bt^2$. Then for current,which statement is incorrect?
$(A)$ decreases linearly with time
$(B)$ reaches a maximum and then decreases
$(C)$ falls to zero after time $t = a/2b$
$(D)$ changes at a rate $-2b$

“In lightning in the sky,there is a steady flow of charge”. -True or False?

Which of the following statements is true about the flow of electrons in an electric circuit?

In conductors,in the absence of an electric field,although electrons are in motion,why is no current formed?

Vedclass Test Series

Exam Paper Generator

Online Exam Module