Question

Calculate the amount of charge flowing in $2$ min in a wire of resistance $10\Omega$ when a potential difference of $20V$ is applied between its ends.
a. $120C$
b. $240C$
c. $20C$
d. $4C$

Answer 1

Hint: By applying Ohm’s law, we can solve this problem. Here, the current is flowing through a wire of resistance $10\Omega $. A potential difference $20V$ is applied between the ends of the wire. We have to calculate the amount of charge flowing through the wire in $2$ minutes. We directly find the current using Ohm’s law and the charge can be obtained from it.

Formula used:
$I = \dfrac{V}{R}$
Where $I$ stands for the current flowing through the wire,
$V$stands for the potential difference, and
$R$ stands for the resistance of the conducting wire.
$q = It$
Where $q$ stands for the amount of charge flowing through the conductor, and
$t$ stands for the time.

Complete step by step answer:
The resistance of the wire is given by $R = 10\Omega $
The potential difference across the ends of the wire is given, $V = 20V$
By applying Ohm’s law, we can find the current as,
$I = \dfrac{V}{R} = \dfrac{{20}}{{10}} = 2A$
The total charge will be,
$q = It$
The time is given as
$t = 2\min = 2 \times 60 = 120s$
The total current is, $I = 2A$
Therefore, the total charge can be written as,
$q = It = 2 \times 120 = 240C$

Hence, the correct answer is option (B).

Additional Information:
According to Ohm’s law, the amount of current flowing through a conductor will be directly proportional to the potential difference across the ends of the conductor. Only when a steady current flows through a conductor, Ohm’s law holds good. Conductors that obey Ohm's law are called ohmic conductors and conductors that do not obey Ohm’s law are called non-ohmic conductors.

Note: The rate of flow of charges across any cross-sectional area of a conductor is defined as an electric current. The flow of current will be in the direction of the flow of positive charge. Therefore we can say that the direction of the current will be opposite to the direction of the flow of electrons.