Question:
25 capacitors each of capacitance \(1\ \mu\text{F}\) are connected in series to a battery of \(100\ \text{V}\). The total charge stored on the capacitors is
25 capacitors each of capacitance \(1\ \mu\text{F}\) are connected in series to a battery of \(100\ \text{V}\). The total charge stored on the capacitors is
Show Hint
For \(n\) identical capacitors in series,
\[
C_{\text{eq}}=\frac{C}{n}.
\]
The charge on every capacitor in a series combination is the same and is given by
\[
Q=C_{\text{eq}}V.
\]
Updated On: Jun 26, 2026
- \(2.0\times10^{-5}\ \text{C}\)
- \(2.5\times10^{-3}\ \text{C}\)
- \(4.0\times10^{-6}\ \text{C}\)
- \(1.5\times10^{-6}\ \text{C}\)
Show Solution
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The Correct Option is C
Solution and Explanation
Step 1: Find the equivalent capacitance of the series combination.
For \(n\) identical capacitors connected in series, \[ C_{\text{eq}}=\frac{C}{n}. \] Given, \[ C=1\ \mu\text{F}=10^{-6}\ \text{F} \] and \[ n=25. \] Therefore, \[ C_{\text{eq}} = \frac{10^{-6}}{25}. \] \[ C_{\text{eq}} = 4\times10^{-8}\ \text{F}. \]
Step 2: Use the relation between charge and capacitance.
The charge stored in a capacitor is \[ Q=CV. \] For the series combination, \[ Q=C_{\text{eq}}V. \] Given, \[ V=100\ \text{V}. \] Hence, \[ Q=(4\times10^{-8})(100). \] \[ Q=4\times10^{-6}\ \text{C}. \]
Step 3: Interpretation of charge in a series combination.
In a series combination, the magnitude of charge on each capacitor is the same and is equal to the charge on the equivalent capacitor.
Therefore, the charge stored on each capacitor as well as the series combination is \[ 4\times10^{-6}\ \text{C}. \]
Step 4: Final conclusion.
Hence, the total charge stored is \[ \boxed{4.0\times10^{-6}\ \text{C}} \] Therefore, the correct option is \[ \boxed{(3)} \]
For \(n\) identical capacitors connected in series, \[ C_{\text{eq}}=\frac{C}{n}. \] Given, \[ C=1\ \mu\text{F}=10^{-6}\ \text{F} \] and \[ n=25. \] Therefore, \[ C_{\text{eq}} = \frac{10^{-6}}{25}. \] \[ C_{\text{eq}} = 4\times10^{-8}\ \text{F}. \]
Step 2: Use the relation between charge and capacitance.
The charge stored in a capacitor is \[ Q=CV. \] For the series combination, \[ Q=C_{\text{eq}}V. \] Given, \[ V=100\ \text{V}. \] Hence, \[ Q=(4\times10^{-8})(100). \] \[ Q=4\times10^{-6}\ \text{C}. \]
Step 3: Interpretation of charge in a series combination.
In a series combination, the magnitude of charge on each capacitor is the same and is equal to the charge on the equivalent capacitor.
Therefore, the charge stored on each capacitor as well as the series combination is \[ 4\times10^{-6}\ \text{C}. \]
Step 4: Final conclusion.
Hence, the total charge stored is \[ \boxed{4.0\times10^{-6}\ \text{C}} \] Therefore, the correct option is \[ \boxed{(3)} \]
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