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.

Given:

A $12\ V$ battery is connected across an unknown resistor, there is a current of 2.5 mA in the circuit.

To find:

To find the value of the resistance of the resistor.

Solution:

It is given that,

The potential difference, $V=12\ V$

Current, $I=2.5\ mA$

We have to find the resistance, $R=?$

By Ohm's Law, $\mathrm{V}=\mathrm{IR}$

On submitting the given values of $V$ and $I$ in the above relationship:

$12=2.5 \times 10^{-3} \times R$ [$I=2.5 \ mA= 2.5 \times 10^{-3} A$]

Or $R=\frac{12}{2.5\times10^{-3}}$

$\mathrm{R}=4.8 \times 10^{3}\ \Omega$

Therefore, the value of the resistance of the resistor is $4.8 \times 10^{3}\ \Omega$.

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