A battery of emf 6V supplies current through a circuit in which resistance can be changed. A high resistance voltmeter is connected across the battery. When the current is 3A, the... A battery of emf 6V supplies current through a circuit in which resistance can be changed. A high resistance voltmeter is connected across the battery. When the current is 3A, the voltmeter reads 5.4V. Find the internal resistance of the battery.
Understand the Problem
The question is asking us to find the internal resistance of a battery given its emf, the current flowing through the circuit, and the voltage reading on a voltmeter. We can use the relationship between emf, current, resistance, and internal resistance to solve for the internal resistance of the battery.
Answer
The internal resistance of the battery is calculated as $r = \frac{E - V}{I}$.
Answer for screen readers
The internal resistance of the battery is given by the formula:
$$ r = \frac{E - V}{I} $$
Steps to Solve
- Identify the given values
Let’s define the variables based on the problem:
- Let $E$ be the electromotive force (emf) of the battery.
- Let $I$ be the current flowing through the circuit.
- Let $V$ be the voltage reading on the voltmeter.
- Let $r$ be the internal resistance of the battery.
Using Ohm's Law and the relationship between these variables, we can write the equation:
$$ E = V + I \cdot r $$
- Rearrange the equation
To solve for the internal resistance $r$, we need to isolate it in the equation. We can rearrange the equation as follows:
$$ I \cdot r = E - V $$
- Solve for internal resistance
Next, divide both sides of the equation by the current $I$:
$$ r = \frac{E - V}{I} $$
- Substitute the values and calculate
Now, substitute the known values of $E$, $V$, and $I$ into the equation we derived, and calculate the internal resistance.
The internal resistance of the battery is given by the formula:
$$ r = \frac{E - V}{I} $$
More Information
The internal resistance of a battery affects its performance, as higher internal resistance means more energy is lost as heat within the battery. Understanding this is crucial for optimizing battery life and efficiency.
Tips
- Failing to correctly rearrange the equation can lead to incorrect results.
- Mixing up the values for emf, current, and voltage can also result in calculation errors. Always double-check that the values are correct and clearly defined before substituting them into formulas.