Series Combination of Capacitors

There are many such electrical and electronic component that use the capacitors.

Home appliances such as TV, fan use the capacitor.

The direct current or supply uses the capacitors in the parallel to eliminate the ripples.

The capacitive voltage divider uses the capacitor in the series.

The connection of the capacitor in the circuit depends on the requirement of the capacitance.

If it is required to increase the effective capacitance in the circuit the capacitors are connected in parallel.

When it is required to decrease the effective capacitance in the circuit, the capacitors are connected in the series.

Let's find the effective capacitance of the capacitors connected in series.

Consider three capacitors connected in series in a circuit with a voltage source of voltage .

Suppose the capacitance of the capacitors is , and respectively.

When the capacitors are connected in series, the charge supplied by the source in the circuit is that remains the same for all the capacitors.

The plates of the capacitor connected to the positive and negative terminal of the battery get accumulated with the positive and negative charge respectively.

'And' due to the induction opposite charge is generated in the subsequent plates.

The voltage drop across the three capacitors connected in series is , and respectively.

Thus, the voltage of the source will be as given,

The relation among capacitance (C), voltage (V) and the Charge(q) are as given above.

The capacitance of the circuit is known as the equivalent capacitance or effective capacitance with which all the capacitances in the circuit can be replaced.

Let the equivalent or effective capacitance for the combination be which is as given above,

From the relation , the voltage drop across the capacitors, , & can be written as above,

Putting the value of , , & in the equation of voltage and we have got,

Therefore, the effective capacitance of the capacitor in the series circuit is given as above,

If capacitors are connected in the series, the effective capacitance of the capacitor will be as above,

The equivalent capacitance of the capacitors connected in series is less than the capacitance of anyone capacitor.

Revision

The direct current or supply uses the capacitors in the parallel to eliminate the ripples.

The capacitive voltage divider uses the capacitor in the series.

If capacitors are connected in the series, the effective capacitance of the capacitor will be as above,

The equivalent capacitance of the capacitors connected in series is less than the capacitance of anyone capacitor.

The End