Two capacitors of `1muF and 2muF` are connected in series and this combination is charged upto a potential difference of 120 volt. What will be the potential difference across 1 micro farad capacitor ?

Options

A. 40 volt
B. 60 volt
C. 80 volt
D. 120 volt

Answer

To solve the problem of finding the potential difference across the 1 microfarad capacitor when two capacitors (1 µF and 2 µF) are connected in series and charged to a potential difference of 120 volts, we can follow these steps:

### Step 1: Calculate the Equivalent Capacitance
For capacitors in series, the formula for equivalent capacitance \(C_s\) is given by:

\[ \frac{1}{C_s} = \frac{1}{C_1} + \frac{1}{C_2} \]

Where:
- \(C_1 = 1 \, \mu F\)
- \(C_2 = 2 \, \mu F\)

Substituting the values:

\[ \frac{1}{C_s} = \frac{1}{1} + \frac{1}{2} = 1 + 0.5 = 1.5 \]

Thus,

\[ C_s = \frac{1}{1.5} = \frac{2}{3} \, \mu F \]

### Step 2: Calculate the Total Charge Stored
The total charge \(Q\) stored in the capacitors can be calculated using the formula:

\[ Q = C_s \cdot V \]

Where:
- \(V = 120 \, V\)

Substituting the values:

\[ Q = \left(\frac{2}{3} \, \mu F\right) \cdot 120 \, V = \frac{240}{3} \, \mu C = 80 \, \mu C \]

### Step 3: Calculate the Potential Difference Across the 1 µF Capacitor
The potential difference \(V_1\) across the 1 µF capacitor can be calculated using the formula:

\[ V_1 = \frac{Q}{C_1} \]

Substituting the values:

\[ V_1 = \frac{80 \, \mu C}{1 \, \mu F} = 80 \, V \]

### Conclusion
The potential difference across the 1 microfarad capacitor is **80 volts**.

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