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. $4C$

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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.

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).