capacitor of 3C & 2C iare joined in series with breakdown voltage of 1kV and 2Kv respectively.calculate source voltage

To solve the problem of finding the source voltage when two capacitors are connected in series, we need to consider both their capacitance values and their breakdown voltages. In this case, we have a 3 microfarad (3C) capacitor and a 2 microfarad (2C) capacitor, with breakdown voltages of 1 kV and 2 kV, respectively. Let's break down the steps to find the total source voltage.

Understanding Series Capacitors

When capacitors are connected in series, the total capacitance (C_total) can be calculated using the formula:

• 1/C_total = 1/C1 + 1/C2

For our capacitors:

• C1 = 3 microfarads (3C)
• C2 = 2 microfarads (2C)

Calculating Total Capacitance

Plugging in the values:

• 1/C_total = 1/3 + 1/2

To combine these fractions, we need a common denominator, which is 6:

• 1/C_total = 2/6 + 3/6 = 5/6

Now, taking the reciprocal gives us:

• C_total = 6/5 microfarads = 1.2 microfarads

Determining Breakdown Voltage

The breakdown voltage of capacitors in series is the sum of their individual breakdown voltages. Therefore:

• V_breakdown_total = V1 + V2

Substituting the values:

• V1 = 1 kV
• V2 = 2 kV

Thus:

• V_breakdown_total = 1 kV + 2 kV = 3 kV

Calculating Source Voltage

The source voltage must not exceed the total breakdown voltage of the series combination of capacitors. Therefore, the maximum source voltage that can be applied without causing breakdown is:

• V_source = V_breakdown_total = 3 kV

Final Result

In conclusion, the source voltage that can be safely applied to the series combination of a 3 microfarad capacitor with a breakdown voltage of 1 kV and a 2 microfarad capacitor with a breakdown voltage of 2 kV is:

• 3 kV

This ensures that neither capacitor exceeds its breakdown voltage, maintaining the integrity of the circuit.