Question

a) Write down the formula which relates electric charge, time and electric current.
b) A radio set draws a current of $0.36A$ for $15$ minutes. Calculate the amount of electric charge that flows through the circuit.

Answer 1

Hint: First of all, we have to define what an electric charge is. With the help of the definition, deduce the formula of the electric charge. For the second part of the question, use the deduced formula of electric charge to find the amount of electric charge flowing through the circuit. Remember, we should first convert the time in minutes to seconds before using it in the formula.

Complete answer:
a) Electric charge is a physical property of the matter. An atom consists of three subatomic particles. They are electrons, protons & neutrons. An electron is negatively charged, a proton is positively charged and a neutron is neutral, i.e. it doesn’t have any charge. Thus electric charges are of two types: positive and negative. Therefore electric charge is defined as the property of the subatomic particles which when placed in an electric & magnetic field experience a force. It is often denoted by $'Q'$. Coulomb is the S.I. unit of the electric charge.
When a current of $1A$ flows through a unit cross-sectional area for one second then the charge is said to be of one coulomb. Mathematically, it can be shown as:
$Q = I.t......(1)$
Where,
$Q$ is the charge.
$I$ is the current.
$t$ is the time.

b) For this section, we have to use equation (1). Let the charge$'Q'$flows through the circuit. The current and the time is given in the question as:
$I = 0.36A$
$t = 15\,{\text{minutes}}$
First, we have to convert the time from minutes to seconds. We know that,
$1\,{\text{minute}} = 60\,{\text{seconds}}$
Therefore the number of seconds in $15\,{\text{minutes}}$ would be,
$15\,{\text{minutes}} = 60\, \times 15\,{\text{seconds}}$
$ \Rightarrow 15\,{\text{minutes}} = 900\,{\text{seconds}}$
Hence time , $t = 900\,\sec $.
Using equation (1) and putting the values of current and time we get,
$Q = 0.36 \times 900$
$ \Rightarrow Q = 324C$
Hence, the electric charge of $324C$ flows through the circuit.

Note:
The electric charges are quantized. This means that the charges cannot take any arbitrary value and only have values that are integral multiples of the fundamental charge, i.e. charge of an electron. Mathematically,
$Q = ne$
Where,
$Q$ is the charge.
$n$ is the integral number.
$e$ is the charge of the electron.
The magnitude charge of an electron is $1.6 \times {10^{ - 19}}C$.