A battery is attached across several different capacitors connected in series. Which of the following statements are true?
1
The capacitor with the largest capacitance carries the largest charge. All the capacitors have the same charge, and the equivalent capacitance is greater than any of the individual capacitors in the group. The largest potential difference appears across the capacitor having the largest capacitance. The largest potential difference appears across the capacitor with the smallest capacitance. The potential difference across each capacitor must be the same. All the capacitors have the same charge, and the equivalent capacitance is less than the capacitance of any of the individual capacitors in the group.
the answers would be:
True: All the capacitors have the same charge, and the equivalent capacitance is less than the capacitance of any of the individual capacitors in the group.
True:The largest potential difference appears across the capacitor with the smallest capacitance.
I will be happy to critique your thinking.
Well, let me enlighten you with some electrifying humor!
First of all, it's shocking to think that the capacitor with the largest capacitance carries the largest charge. Don't worry, all the capacitors get along just fine and have the same charge!
Now, when it comes to the potential difference, it's like a game of musical chairs. The largest potential difference appears across the capacitor with the largest capacitance! It's like the star of the show, stealing all the voltage limelight.
But wait, there's a twist! Despite the potential difference preferences, all the capacitors in this series act like equal partners. They all have the same potential difference, and they're all charged up about it.
And now for the grand finale: when it comes to the equivalent capacitance, it's neither greater nor smaller than any individual capacitor. It's like a balancing act, finding the right equilibrium to keep everything in harmony.
So in summary, the true statements are:
- All the capacitors have the same charge.
- The largest potential difference appears across the capacitor with the largest capacitance.
- The potential difference across each capacitor must be the same.
- The equivalent capacitance is neither greater nor smaller than any individual capacitor.
Hope that charged you up with some humor and knowledge!
To determine which statements are true, let's analyze the behavior of capacitors connected in series and the relationship between capacitance, charge, and potential difference.
When capacitors are connected in series, they share the same charge, but the potential difference across each capacitor may differ. The total capacitance of the series combination is given by the reciprocal of the sum of the reciprocals of the individual capacitances.
Let's evaluate each statement:
1. The capacitor with the largest capacitance carries the largest charge.
FALSE. In a series combination, all capacitors have the same charge. This is because they are connected in series, so the current passing through each capacitor is the same, resulting in an equal charge accumulation.
2. All the capacitors have the same charge, and the equivalent capacitance is greater than any of the individual capacitors in the group.
FALSE. All the capacitors in a series combination have the same charge, but the equivalent capacitance is always less than the capacitance of any individual capacitor. The formula for equivalent capacitance in a series combination is the reciprocal of the sum of the reciprocals of individual capacitances.
3. The largest potential difference appears across the capacitor having the largest capacitance.
TRUE. In a series combination, the potential difference across each capacitor depends on its capacitance. The capacitor with the largest capacitance will have the largest potential difference across it.
4. The largest potential difference appears across the capacitor with the smallest capacitance.
FALSE. The potential difference across each capacitor in a series combination increases as the capacitance of the capacitor decreases. Therefore, the capacitor with the smallest capacitance will have the largest potential difference across it.
5. The potential difference across each capacitor must be the same.
FALSE. In a series combination, the potential difference across each capacitor will be different since it depends on the capacitance of the individual capacitors.
6. All the capacitors have the same charge, and the equivalent capacitance is less than the capacitance of any of the individual capacitors in the group.
TRUE. As mentioned earlier, all capacitors in a series combination have the same charge. The equivalent capacitance is always less than the capacitance of any individual capacitor.
Based on this analysis, the true statements are:
- The largest potential difference appears across the capacitor having the largest capacitance.
- All the capacitors have the same charge, and the equivalent capacitance is less than the capacitance of any of the individual capacitors in the group.