Question

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

Answer 1

Step 1: Given data

There is a current of $2.5\mathrm{mA}$ in the circuit because a $12\mathrm{V}$ battery is connected across an unknown resistance.

$$\begin{gathered} \mathrm{V}=12\mathrm{V} \\ \mathrm{I}=2.5\mathrm{mA} \\ =2.5\times {10}^{-3}\mathrm{A} \end{gathered}$$

Step 2: Formula used

Let R be the resistance.

If all physical conditions and temperatures stay constant, Ohm's law asserts that the voltage across a conductor is directly proportional to the current flowing through it.

The resistance (R) of a resistor is defined by Ohm's law.

$\mathrm{V}=\mathrm{IR}$

Step 3: Calculate the resistance

By putting the value of V and I in Ohm's law,

$$\begin{gathered} 12=2.5\times {10}^{-3}\mathrm{R} \\ \mathrm{R}=4.8\times {10}^3\mathrm{\Omega } \end{gathered}$$

As a result, the resistor's resistance is $4.8\times {10}^3\Omega$.