Question:
The charge flowing in a conductor varies with time as $ Q=at-b{{t}^{2}}, $ then the current changes at the rate of $ (-2b) $ falls to zero after $ T=\left( \frac{a}{2b} \right) $ (3) reaches a maximum and then decreases (4) will remain constant
The charge flowing in a conductor varies with time as $ Q=at-b{{t}^{2}}, $ then the current changes at the rate of $ (-2b) $ falls to zero after $ T=\left( \frac{a}{2b} \right) $ (3) reaches a maximum and then decreases (4) will remain constant
Updated On: Jun 20, 2022
- 1, 2 and 3 are correct
- 1 and 2 are correct
- 2 and 4 are correct
- 1 and 3 are correct
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The Correct Option is B
Solution and Explanation
$ Q=at-b{{t}^{2}} $ Current, $ I=\frac{dQ}{dt} $
$=\frac{d}{dt}(at-b{{t}^{2}}) $
$=a-2bt $ If $ I=0 $ then $ 0=a-2bt $ or $ t=\frac{a}{2b} $ Also, $ \frac{dI}{dt}=\frac{d}{dt}(a-2bt) $
$=-2b $
Therefore, current change at the ratio of $ (-2b) $ .
$=\frac{d}{dt}(at-b{{t}^{2}}) $
$=a-2bt $ If $ I=0 $ then $ 0=a-2bt $ or $ t=\frac{a}{2b} $ Also, $ \frac{dI}{dt}=\frac{d}{dt}(a-2bt) $
$=-2b $
Therefore, current change at the ratio of $ (-2b) $ .
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Concepts Used:
Electric Current
Defining Electric Current
It is the rate of flow of electrons in a conductor. SI Unit - Ampere (A).
Electrons are negatively charged particles hence when they move a number of charges moves.
Note:- The ability of a particular substance to conduct electricity depends on the number of electrons that are able to move . Some of the materials allow current to flow better than others.
What is an Electromotive Force?
If a force acts on electrons to make them move in a particular direction, then up to some extent random motion of the electrons will be eliminated. An overall movement in one direction. The force which acts on the electrons to move them in a certain direction is known as electromotive force and its quantity is known as voltage and is measured in V.