Question

A battery that contains emf e and internal resistance r when connected across an external resistance of 12 ohm, produces a current of 0.5 a. when connected across a resistance of 25 ohm, it produces a current of 0.25 a. find

internal resistance and

Answer 1

To determine the internal resistance of a battery, set up two equations using Ohm's Law and the terminal voltage formula, based on two occurrences with different external resistances and currents, then solve the system of equations.

Step-by-step explanation:

To find the internal resistance r of a battery given two scenarios where it drives different currents through different external resistances, we use Ohm's Law and the formula for terminal voltage. The terminal voltage V of a battery when current is flowing can be given as V = emf - Ir, where I is the current and r is the internal resistance. We have two equations based on the two different external resistances and the two different currents.

• With a 12 ohm resistor drawing 0.5 A: emf = Ir + V where V = I * 12 ohms
• With a 25 ohm resistor drawing 0.25 A: emf = Ir + V where V = I * 25 ohms

By substituting the values of I and V in each equation, we can form a system of two equations with two variables (emf and r). Solving this system will give us the values for emf and the internal resistance r.