Question

The voltage across the terminals of a 9.0V battery is 8.3V when the battery is connected to a 60? load.

What is the battery's internal resistance?

Answer 1

Concepts and reason

The concepts used to solve this problem are Ohm’s law and Kirchhoff’s loop rule.

Initially, the current flowing through the circuit can be calculated by using the ohm’s law equation by substituting potential and resistance. Later the internal resistance of the battery can be calculated by using Kirchhoff’s loop rule by relating the equation with emf, internal resistance, current and resistance.

Fundamentals

At constant temperature, the steady current flow through the circuit is directly proportional to the potential developed across the circuit gives the ohm’s law.

The relation between the current and potential difference from the ohm’s law is,

Here, is the current flow through the circuit, is the voltage, andis the external load resistance.

From Kirchhoff’s loop rule, the loop equation for the internal resistance of the battery is,

$&-Ir-IR=0 $

Here, is the internal resistance of the battery and is the emf of the battery.

According to the ohm’s law,

The expression can be rewrite for the current flow through the circuit,

Substitute for and for to find I.

According to Kirchhoff’s loop rule, the loop equation for the internal resistance of the battery is,

$&-Ir-IR=0 $

The expression can be rewrite for the internal resistance of the battery,

Substitute for , for , and for to find r.

Ans:

The internal resistance of the battery is .