The voltage across the terminals of a 7 V battery is 6.77 V when the battery is connected to a 18.3 Ω load. What is the battery's internal resistance? (in Ω)


To determine the internal resistance \( r \) of the battery, we can use the following relationship:

\[
V_{\text{battery}} = V_{\text{load}} + V_{\text{internal}}
\]

Where:
- \( V_{\text{battery}} = 7 \, \text{V} \) (the battery's open-circuit voltage)
- \( V_{\text{load}} = 6.77 \, \text{V} \) (the voltage across the load)
- \( V_{\text{internal}} = I \cdot r \) (the voltage drop due to internal resistance)

The current \( I \) flowing through the circuit can be found using Ohm's law:

\[
I = \frac{V_{\text{load}}}{R_{\text{load}}}
\]

Where:
- \( R_{\text{load}} = 18.3 \, \Omega \)

Once we find the current, we can calculate the internal resistance using the fact that the voltage drop across the internal resistance is the difference between the battery's open-circuit voltage and the voltage across the load:

\[
r = \frac{V_{\text{battery}} - V_{\text{load}}}{I}
\]

Let's calculate this step by step.

### Step 1: Calculate the current \( I \)
\[
I = \frac{6.77}{18.3}
\]

### Step 2: Calculate the internal resistance \( r \)
\[
r = \frac{7 - 6.77}{I}
\]

Now, I'll compute this.The internal resistance of the battery is approximately \( 0.622 \, \Omega \).

Would you like further details on this process, or do you have any questions?

Here are some related questions to deepen understanding:
1. How would the internal resistance affect the performance of a battery in a real-world scenario?
2. What happens to the power delivered to the load as the internal resistance increases?
3. How could you experimentally determine the internal resistance of a battery?
4. How does the internal resistance vary with temperature?
5. What is the significance of internal resistance in rechargeable versus non-rechargeable batteries?

**Tip:** As internal resistance increases, more energy is wasted as heat within the battery, reducing its efficiency in delivering power to the external load.

The voltage across the terminals of a 7 V battery is 6.77 V when the battery is connected to an 18.3 Ω load. What is the battery's internal resistance? (in Ω)

Learn how to calculate the internal resistance of a battery with a 7 V open-circuit voltage and a voltage of 6.77 V across an 18.3 Ω load. This problem involves Ohm's Law and electric circuits, suitable for Grades 11-12 students.

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