Question

An electrical appliance has a resistance of 4 ohms. When it is connected to a 12V battery, the number of coulombs passing through it per second is
A. 1.2
B. 12
C. 0.3
D. 3

Answer 1

Hint:The current in the circuit is the number of charges flowing through a given cross section per unit time. The number of coulombs per second is the current in the circuit. Using Ohm’s law, calculate the current in the circuit.

Formula used:
Ohm’s law, \[V = IR\]
where, V is the voltage, I is the current and R is the resistance.

Complete step by step answer:
We define the current in the circuit as the number of charges flowing through given cross section per unit time. Since the charge is measured in units of coulomb, we have the unit of current as,
\[I\left( A \right) = \dfrac{{q\left( C \right)}}{{t\left( s \right)}}\]
Here, q is the charge in the coulomb and t is the second.
Since we are asked to determine the number of coulomb per second, we have to calculate the current in the circuit. We have given that the resistance of the circuit is \[R = 4\,\Omega \] and the emf of the battery is\[V = 12\,{\text{V}}\].
We have from Ohm’s law, the voltage is proportional to the current in the circuit. Therefore,
\[V = IR\]
\[ \Rightarrow I = \dfrac{V}{R}\]
Here, V is the voltage, I is the current and R is the resistance.
Substituting \[V = 12\,{\text{V}}\] and \[R = 4\,\Omega \] in the above equation, we get,
\[I = \dfrac{{12}}{4}\]
\[ \therefore I = 3\,{\text{A}}\]
Thus, the number of coulomb per second passing through the circuit is 3.

So, the correct answer is option D.

Note:The current in the circuit supplied by the battery depends on the value of resistance. Increasing resistance restricts the flow of current through the circuit. The current in the circuit is expressed as the rate of flow of charge per unit time. The charge supplied by the battery remains conserved in the series circuit.