Question

A current of \[5\] amperes is passed through a metallic conductor. The charge flowing in one minute in coulombs will be
A. $5\,C$
B. $12\,C$
C. $\dfrac{1}{{12}}\,C \\ $
D. $300\,C$

Answer 1

Hint: To solve this question we will use the definition of current flowing through a conductor in a given period of time. Current is defined as the rate of flow of charges through an area of cross section. This definition suggests that current is total charge divided by the time taken for the flow of charge through a given area of cross section. We will use this to find the required value of charge flowing through the given metallic conductor.

Formula used:
The formula of current in terms of charge and time is,
$I = \dfrac{Q}{t}$
where $I$ is the current flowing through the conductor, $Q$ is the total charge, $t$ is the time for which the current flows.

Complete step by step solution:
Given: Current flowing through the given metallic conductor is $I = 5A$
Time for which the current flows is $t = 1\min $
Converting time into SI units, we get $t = 60\sec $

Now we know that a stream of charged particles, such as electrons or ions, travelling through an electrical conductor or a vacuum constitutes an electric current. Therefore,
$I = \dfrac{Q}{t}$ . . . (1)
From equation (1), we get;
$Q = I \times t$ . . . (2)
On substituting the given values in equation (2), we get;
$Q = 5 \times 60$
$\therefore Q = 300C$

Hence, option D is the correct answer.

Note: One should remember that $Q$ is the total charge flowing in the conductor and not the charge on a single electron. Also convert the unit of time into SI unit (here, from minute to seconds) otherwise we will not get the answer in coulombs rather the answer could come in unit $A\,\min $ , that is, ampere minute.