Question

Three capacitors c1 c2 c3 are connected in series derive an expression for the equivalent capacitance

Answer 1

Here Given :-

Three capacitors C1,C2,C3 and these are connected in series

To Derive:-

The equivalent capacitance of three capacitors c1,c2, and c3 connected in series

Solution:-

• We have three capacitors and assume that the voltage of the battery is v(volt). After connecting the battery to the capacitors in series ,the electronic charge i.e. (-q)  will be transferred from negative terminal to the right of plate of c3 and same is done for the plate of c2 also due to the electrostatic induction force.

• While the positive plate of c2 induces the (+q) amount of charge to the left plate of c1 and at last the electronic charge (-q)  will transferred from left plate of c1 to the positive terminal of the battery.

• Since the three capacitors are different so they will have different voltages let say v1 , v2, v3 respectively and by the above processes the amount of charge on each capacitors will be same i.e. q

And here the total Voltage of the battery will be equal to the sum of each voltage of a single capacitor  

                        V= v1 +v2 +v3     (let say eq1)

  we know that Q= CV or  V =Q/C

                        V= q/c1 +q/c2 +q/c3  ( from eq1)

          V/q = 1/c1 + 1/c2 +1/c3   (   Because V is the total voltage of the battery and q is the total charge so V/q will be the Ceq i.e. the equivalent capacitance)

    The required expression for the equivalent capacitance of three capacitors connected in series is   1/Ceq = 1/c1 +1/c2 +1/c3