Answer
417.9k+ views
Hint To solve this question, we need to compute the current flowing through the body by using its basic formula. For this we have to calculate the charge flowing through the body per second from the value of the number of electrons given. Finally, using the values of the current thus obtained, and the value of the charge given, we can get the value of the time required.
The formula which is used in solving this question is given by
$\Rightarrow I = \dfrac{{dq}}{{dt}}$, here $I$ is the current, $q$ is the charge, and $t$ is the time.
Complete step by step answer
We know that the current through a conductor is defined as the rate of flow of charge through it. Mathematically, it can be expressed as
$\Rightarrow I = \dfrac{{dq}}{{dt}}$ (1)
Now, we know that the total charge contained by a given number of electrons is given by
$\Rightarrow q = ne$
According to the question, we have $n = {10^{18}}$. Also we know that $e = 1.6 \times {10^{ - 19}}C$. Substituting these above we get
$\Rightarrow q = {10^{18}} \times 1.6 \times {10^{ - 19}}$
On solving, we get
$\Rightarrow q = 0.16C$
According to the question, this much amount of charge is taken out every second from the body. So we have
$\Rightarrow dq = 0.16C$, and
$\Rightarrow dt = 1s$
Substituting these in (1) we get
$\Rightarrow I = \dfrac{{0.16}}{1}$
$\Rightarrow I = 0.16A$ (2)
Now, from (1) we have
$\Rightarrow I = \dfrac{{dq}}{{dt}}$
Multiplying both sides by $dt$ we have
$\Rightarrow Idt = dq$
From (2)
$\Rightarrow 0.16dt = dq$
Integrating both sides, we get
$\Rightarrow 0.16\int\limits_0^T {dt} = \int\limits_0^Q {dq} $
$\Rightarrow 0.16\left[ t \right]_0^T = \left[ q \right]_0^Q$
On substituting the limits we get
$\Rightarrow 0.16T = Q$
$\Rightarrow T = \dfrac{Q}{{0.16}}$
According to the question, we have $Q = 0.1C$. So we get
$\Rightarrow T = \dfrac{{0.1}}{{0.16}}$
$\Rightarrow T = 0.625s$
Thus, the time required to get a total charge of $0.1C$ from the body is equal to $0.625s$.
Hence, the correct answer is option A.
Note
Instead of calculating the current, we could have used the unitary method to solve this question also. As we are given the amount of charge flowing in one second, so we can calculate the time required to get the given amount of charge by the unitary method.
The formula which is used in solving this question is given by
$\Rightarrow I = \dfrac{{dq}}{{dt}}$, here $I$ is the current, $q$ is the charge, and $t$ is the time.
Complete step by step answer
We know that the current through a conductor is defined as the rate of flow of charge through it. Mathematically, it can be expressed as
$\Rightarrow I = \dfrac{{dq}}{{dt}}$ (1)
Now, we know that the total charge contained by a given number of electrons is given by
$\Rightarrow q = ne$
According to the question, we have $n = {10^{18}}$. Also we know that $e = 1.6 \times {10^{ - 19}}C$. Substituting these above we get
$\Rightarrow q = {10^{18}} \times 1.6 \times {10^{ - 19}}$
On solving, we get
$\Rightarrow q = 0.16C$
According to the question, this much amount of charge is taken out every second from the body. So we have
$\Rightarrow dq = 0.16C$, and
$\Rightarrow dt = 1s$
Substituting these in (1) we get
$\Rightarrow I = \dfrac{{0.16}}{1}$
$\Rightarrow I = 0.16A$ (2)
Now, from (1) we have
$\Rightarrow I = \dfrac{{dq}}{{dt}}$
Multiplying both sides by $dt$ we have
$\Rightarrow Idt = dq$
From (2)
$\Rightarrow 0.16dt = dq$
Integrating both sides, we get
$\Rightarrow 0.16\int\limits_0^T {dt} = \int\limits_0^Q {dq} $
$\Rightarrow 0.16\left[ t \right]_0^T = \left[ q \right]_0^Q$
On substituting the limits we get
$\Rightarrow 0.16T = Q$
$\Rightarrow T = \dfrac{Q}{{0.16}}$
According to the question, we have $Q = 0.1C$. So we get
$\Rightarrow T = \dfrac{{0.1}}{{0.16}}$
$\Rightarrow T = 0.625s$
Thus, the time required to get a total charge of $0.1C$ from the body is equal to $0.625s$.
Hence, the correct answer is option A.
Note
Instead of calculating the current, we could have used the unitary method to solve this question also. As we are given the amount of charge flowing in one second, so we can calculate the time required to get the given amount of charge by the unitary method.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)