Question

A current of $150\;{\rm{mA}}$ flows through a circuit for $2\;{\rm{min}}$. Find the amount of charge that flows through the circuit.

Answer 1

Hint: When the current is flowing in the electric circuit, then the magnitude of the current gives us information about the amount of charge that flows in the circuit because of current means the rate of charge flow. So use the expression of current for the determination of the charge magnitude by rearranging the expression of current. After this, we will use the information that is given in the question in the rearranged expression so that we will obtain the answer.

Complete step by step answer:
It is given that the amount of current in the circuit is $150\;{\rm{mA}}$ for time $2\;{\rm{min}}$. So, write the expression of the current.
Therefore, we get
$I = \dfrac{Q}{t}$
Here, $I$ is the current, $Q$ is the charge and $t$ is the time.
Rearrange the above equation to determine the magnitude of the charge, so
$Q = It$
Now, we will get the amount of charge flowing in the circuit by substituting the values in the above equation
Therefore, we get
$ Q = 150\;{\rm{mA}} \times \dfrac{{1 \times {{10}^{ - 6}}\;{{\rm{C}} {\left/{\vphantom {{\rm{C}} {\sec }}} \right.} {\sec }}}}{{1\;{\rm{mA}}}} \times 2\;{\rm{min}} \times \dfrac{{60\;{\rm{sec}}}}{{1\;\min }}\\$
$\implies Q = 1.5 \times {10^{ - 4}}\;{{\rm{C}} {\left/{\vphantom {{\rm{C}} {\sec }}} \right.} {\sec }} \times 120\;{\rm{sec}}\\$
$\implies Q = 0.018\;{\rm{C}}$
Therefore, the amount of charge flows through the circuit is $0.018\;{\rm{C}}$.

Note:
Generally, the common measuring unit used for the measurement of the amount of charge is Coulomb. During the calculation, do the correct unit conversion so that we will obtain the charge in the unit of Coulomb. Here, in this question, a current is given in microampere and time in minutes, so to obtain the charge in the unit of Coulomb, we converted current into Coulomb per second and time into seconds