Question

A parallel combination of a 1.13-μF capacitor and a 2.85-μF one is connected in series to a 4.25-μF capacitor. This three-capacitor combination is connected to a 17.3-V battery. Find the charge of each capacitor.

a) Charge of 4.25-μF capacitor: ______________ C

b) Charge of 1.13-μF capacitor: ______________ C

c) Charge of 2.85-μF capacitor: ______________ C

Answer 1

Concepts and reason

The concepts used to solve this problem are series and parallel combination of capacitors and charge on a capacitor.

First, find the equivalent capacitance for the whole circuit using series and parallel combination.

Then, find the charge on by calculating the total charge of the series combination.

Finally, find the charge on the and by calculating the voltage for the parallel combination.

Fundamentals

In electronic circuits capacitors are the standard components. And it is denoted by .

When capacitors are connected in series,

The equivalent capacitance of the capacitors in series is equal to the sum of inverse of the reciprocals of individual capacitances.

In general the expression for equivalent capacitance in series is,

Here, is the total capacitance and , , are the capacitance.

When capacitors are connected in parallel,

The equivalent capacitance of the capacitors in parallel is equal to the sum of the individual capacitances.

In general the expression for equivalent capacitance in parallel is,

The capacitor is a charge storing device.

The expression for the charge on a capacitor is,

Here, is the charge, is the capacitance, and is the voltage.

(a)

The capacitance and are in parallel.

The expression of for parallel capacitance and is,

Now, the capacitance and are in series.

The expression of for series capacitors and is,

Substitute for .

The expression for the total charge on a capacitor is,

Substitute for and for .

The capacitor and are in series.

In series connection the charges will be same for all capacitors.

So the charge on capacitor is .

(b)

The charge on (i.e.) is in series connection with .

The capacitance and are in parallel. For parallel connection the voltage will be same for the capacitors.

By rearranging the charge on a capacitor expression,

The expression for the voltage of parallel combination capacitors is,

Substitute for and for .

The expression for the charge on the capacitor is,

Substitute for and for

(C)

The expression for the charge on the capacitor is,

Substitute for and for .

Ans: Part a

The charge on capacitor is .

Part b

The charge on capacitor is .

Part c

The charge of capacitor is .