Question

When a 12 V battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit. Find the value of the resistance of the resistor.

Answer 1

Hint: In this question, we first draw the figure according to the question then we write the expression of ohm’s law that is $V = IR$. In the question the values of voltage V is and the value of the current I through the circuit are given so after substituting these values in the ohm’s law formula we can get the value of unknown resistance.

Complete step-by-step solution -
First, we will draw the required circuit that is we connect a 12 V battery in series with a resistance R and it is given that the current flowing through the circuit is 2.5 mA. This circuit is shown in figure 1

Now we know from ohms law which states that the current I in a circuit or between two points is proportional to the voltage V or the potential difference across Resistance between the two points that is
\[I \propto V\]
And the proportionality constant here is the resistance R whose unit is ohm denoted by $\Omega $, that is
$V = IR$----------------------------- (1)
So in this question, we have
$V = 12V$
$I = 2.5mA = 0.0025A$
Now substituting the values of V and I in equation (1) we get
$12V = 0.0025 \times R$
Taking the constant on one side we get
$R = \dfrac{{12V}}{{0.0025A}}$
$R = 4800\Omega = 4.8K\Omega $
Therefore, we are getting the value of the unknown resistance as 4.8 Kilo ohms.

Note: For these types of questions we need to know about the basic of electric circuits that what is ohm’s law and how to apply it, how to apply current divider in parallel circuits, how to apply voltage divider in a series circuit, what is the resistivity of resistance, etc. we also need to take care of the units and the sign conventions in these types of question.