Question

When a 40 V battery is connected across an unknown resistor, there is a current of 100 mA in the circuit. Find the value of resistance of the resistor.
A. \[5000\,\Omega \]
B. \[400\,\Omega \]
C. \[0.8\,\Omega \]
D. None of these

Answer 1

Hint:Convert the current from mA to A. Use Ohm’s law to determine the value of unknown resistance. According to Ohm’s law, the potential difference provided by the battery is proportional to the current in the circuit and the constant of proportionality is the resistance of the circuit.

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

Complete step by step answer:
We have given the emf of the battery \[e = 40\,{\text{V}}\] and the current through the circuit is \[I = 100\,{\text{mA}} = 0.1\,{\text{A}}\] . The quantity we have to calculate is the resistance of the resistor, \[R = ?\].
We have according to Ohm’s law, the potential difference in the circuit is proportional to the current in the circuit and the constant of proportionality is the resistance of the circuit. Therefore, we can write,
\[e = IR\]
Rearranging the above equation for R, we get,
\[R = \dfrac{e}{I}\]
Substituting \[e = 40\,{\text{V}}\] and \[I = 0.1\,{\text{A}}\] in the above equation, we get,
\[R = \dfrac{{40}}{{0.1}}\]
\[ \Rightarrow R = 400\,\Omega \]

Therefore, the value of the unknown resistor is \[400\,\Omega \]. So, the correct answer is option B.

Note: In Ohm’s law, we have taken the emf of battery e instead of voltage V. We could have used voltage V if it is the voltage across the resistor. In this solution, we have neglected the internal resistance of the battery since it will be very small. If you have given the internal resistance of the battery, then you have used Kirchhoff’s voltage law in the circuit to determine the value of unknown resistance.