Answer
Verified
437.7k+ 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
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How do you graph the function fx 4x class 9 maths CBSE
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Give 10 examples for herbs , shrubs , climbers , creepers
Why is there a time difference of about 5 hours between class 10 social science CBSE
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
What is BLO What is the full form of BLO class 8 social science CBSE