## 6 Common Problems of Capacitors

- Category: High School
- Written by fisikastudycenter

physics.fisikastudycenter.com-Learning capacitor in problems and solutions tutorial method. Finding equivalent capacitor in series and parallel combination, energy stored, potential difference across capacitors, electric charge storage, spherical capacitor and parallel plate-capacitors capacitance will be discussed.

**Problem 1**

Given a circuit contents a combination of three capacitors X, Y and Z , see the figure below.

If the switch S is ON, find:

a) circuit equivalent capacitance (equivalent capacitor)

b) electric charge stored in the circuit

c) electric charge stored in capacitor Z, use series principle

d) potential difference across capacitor Z

e) potential difference across capacitor X

f) potential difference across capacitor Y

g) electric charge stored in capacitor X

h) electric charge stored in capacitor Y

i) electric charge stored in capacitor Z

j) energy stored in the circuit

k) energy stored in capacitor X

l) energy stored in capacitor Y

m) energy stored in capacitor Z

**Discussion**

a) First replace X and Y parallel combination by its equivalent capacitance, named C_{xy} :

Replacing the two capacitors gives us the equivalent circuit in series combination, then find the equivalent for C_{xy} and C_{z} , the two are in series, called C_{eq} or C_{tot} :

b) Charge stored in the circuit or the charge in the equivalent capacitance; Q_{tot} , C_{tot} multipled by V_{tot}

c) Charge stored in capacitor Z; Q_{z}

For series combination, the charge is the same on all capacitors, it's the same as the charge on the equivalent capacitor :

d) potential difference across capacitor Z; named V_{z}

e) potential difference across capacitors X and Z are the same cause of parallel combination

f) potential difference across Y is the same as potential difference across X

g) charge in capacitor X, be careful, it's not the same as charge in equivalent capacitor

h) charge in capacitor Y

i) charge in capacitor Z

j) energy stored in the circuit

Use one of these three formula to get the energy stored

So then

k) energy stored in capacitor X

l) energy stored in capacitor Y

m) energy stored in capacitor Z

**Problem ****2**

Given three capacitor in a circuit below, the voltage source is 24 volt.

If the switch is ON, find :

a) circuit equivalent capacitancy

b) electric charge stored in circuit

c) electric charge stored in capacitor Z

d) potential difference across capacitor Z

e) potential difference across capacitor X

f) potential difference across capacitor Y

g) electric charge stored in capacitor X

h) electric charge stored in capacitor Y

i) energy stored in the circuit

j) energy stored in capacitor X

k) energy stored in capacitor Y

l) energy stored in capacitor Z

**Try ..!! ****Problem ****3**

Given a parallel-plate capacitor in vacuum. The plates of capacitor are 2 cm apart and 50 cm^{2} in area of each plate. A potrntial difference of 120 volt is applied acroos capacitor. When ε_{o} is 8,85 x 10^{− 12} C^{2} N ^{− 1} ^{− 2} calculate :

a) capacitor capacitane

b) charge stored in capacitor

c) the magnitude of electric charge in space between the two plates of capacitor

**Answer**

a) capacitor capacitance

b) charge stored in capacitor

c) the magnitude of electric charge in space between the two plates of capacitor

**Problem **** 4**

A plate-capacitor of capacitance C in vacuum. If then a material with its dielectric constant K = 2 is inserted between capacitor plates, find the new capacitance of capacitor!

**Answer**

There are no changing in area and plates separation distance of capacitor, so then the new capacitance is

**Problem ****5**

Given a parallel plate-capacitor of 1200 μF in vacuum. If the area of capacitor plates are doubled and the separation between two plates is 1.5 times the original, find the new capacitance of the capacitor!

**Answer**

**Problem ****6**

A spherical capacitor with its radius of 1.8 cm. When 1/4πε_{o} = 9 x 10^{9} in international unit, find the capacitance of this spherical capacitor!

**Answer**

The capacitance of spherical capacitor with radius of R :