Question

The voltage across the terminals of a 9.0V battery is

8.2V when the battery is connected to a 40Ω load. What is the internal resistance of the battery?

a) 0.8Ω
b) 1.0Ω
c) 1.2Ω
d) 2.0Ω

Answer 1

The calculation involves finding the internal resistance of a battery with a given load using Ohm's law and the formula for terminal voltage. It involves solving the equation V = emf - Ir, where emf is the electromotive force, V is the terminal voltage, I is the current, and r is the internal resistance.

Step-by-step explanation:

The question concerns the calculation of the internal resistance of a battery while a load is connected to it. This falls under the discipline of physics, specifically within the area of electric circuits and Ohm's law. In order to find the internal resistance of the battery, we can apply the formula for terminal voltage, which is V = emf - Ir, where V is the terminal voltage, emf is the electromotive force or the open-circuit voltage of the battery, I is the current through the load, and r is the internal resistance.

First, we calculate the current I using Ohm's law (V = IR), where R is the resistance of the load (40Ω):
I = V / R = 8.2V / 40Ω = 0.205A.

Now, using the formula V = emf - Ir, we can solve for r:
r = (emf - V) / I = (9.0V - 8.2V) / 0.205A ≈ 3.9Ω, which is not listed among the options, indicating that there may have been a typo or error in the question or answer choices.