Question

If a charge of \[420\,C\] flows through a conducting wire in \[5\] minutes what is the value of the current?

Answer 1

Hint: Current is defined as the rate of change of charge. So, charge can be defined as the current flowing through a material in one second (unit time). In the question, the amount of charge flowing through the conducting wire is given along with the time in minutes. Using the apt formula and necessary conversion, we can reach the solution as to find the value of the current flowing through the wire. To get the value of charge in coulomb, we need to convert time to seconds as one ampere is equal to one coulomb per second.

Formula used:
The amount of current flowing through a conducting wire is given by the formula,
\[I = \dfrac{Q}{t}\]

Complete step by step answer:
The following data is given in the question, charge flowing through the conducting wire is given by the formula \[Q = 420\,C\]. Since the value of one minute is equal to \[60\] seconds we multiply the value of time in minutes with \[60\] to convert it into seconds.Time taken for the charge to flow through the conducting wire in seconds is given by,
\[t = 5\min \\
\Rightarrow t= 5 \times 60 \\
\Rightarrow t= 300\,s\]
Using the formula we have,
\[I = \dfrac{Q}{t} \\
\Rightarrow I = \dfrac{{420C}}{{300s}} \\
\therefore I = \dfrac{7}{5}A\]

Hence, the current through a conducting wire carrying a charge of \[420C\] in \[5\] minutes (\[300\] seconds) is \[1.4\,A\].

Note: The conversion from minutes to seconds is crucial, many will forget that part and find the answer in minutes. The value of Ampere is one Coulomb per second and hence the conversion from minutes to seconds is very important.