
Three capacitors of capacitance $2\,pF,3\,pF$ and $4\,pF$ are connected parallel.
(a) What is the total capacitance of the combination?
(b) Determine the change on each capacitor if the combination is connected to 100V supply.
Answer
483.6k+ views
Hint: As three of the capacitors are connected parallelly to each other then sum of all the three capacitors gives us the total capacitance of the combination. As the capacitance is connected parallelly then the voltage across each capacitance will remain the same, now putting the voltage capacitance and charge relation we can find out the charge on each capacitance.
Complete step by step answer:
(a) As per the problem there are three capacitors of capacitance $2pF,3pF$ and $4pF$are connected parallel. When capacitors are connected parallel to each other then their total resistance is calculated by adding all the capacitance.Now we can get,
Total capacitance = capacitance one + capacitance two + capacitance three
Mathematically,
$C = {C_1} + {C_2} + {C_3} \ldots \ldots \left( 1 \right)$
Given,
${C_1} = 2pF$
$\Rightarrow {C_2} = 3pF$
$\Rightarrow {C_3} = 4pF$
Here $pF$ is the unit of capacitance.
PicoFarad = pF
Hence total capacitance,
Putting the given values in equation $\left( 1 \right)$ we get,
$C = 2pF + 3pF + 4pF$
On further solving we get,
$\therefore C = 9\,pF$
Therefore the total capacitance of the combination is $9\,pF$.
(b) As we know the supply voltage to the capacitance is $100V$. Three capacitance is connected parallelly hence voltage will remain same for all the capacitor.We know,
$q = VC \ldots \ldots \left( 2 \right)$
Where, Charge of the capacitor = $q$, Supply Voltage or voltage across capacitor = $V$ and Capacitance = $C$.
Using equation $\left( 2 \right)$ in all the three cases:
For capacitor one we get,
${q_1} = V{C_1}$
Now putting the given values in the equation we get,
${q_1} = 100V \times 2pF$
We know,
$1pF = {10^{ - 12}}F$
Now the change become,
${q_1} = 100V \times 2 \times {10^{ - 12}}F$
$\Rightarrow {q_1} = 2 \times {10^{ - 10}}C$
Unit is coulomb.
Similarly, for charge two we get,
${q_2} = V{C_2}$
Now putting the given values in the equation we get,
${q_2} = 100V \times 3pF$
$ \Rightarrow {q_2} = 100V \times 3 \times {10^{ - 12}}F$
$ \Rightarrow {q_2} = 3 \times {10^{ - 10}}C$
For charge three we get,
${q_3} = V{C_3}$
Now putting the given values in the equation we get,
${q_3} = 100V \times 4pF$
$ \Rightarrow {q_3} = 100V \times 4 \times {10^{ - 12}}F$
$ \Rightarrow {q_3} = 4 \times {10^{ - 10}}C$
Hence, upon keeping the supply voltage to the all three capacitors at $100V$, we can observe only change in their charges as $2 \times {10^{ - 10}}C$, $3 \times {10^{ - 10}}C$ and $4 \times {10^{ - 10}}C$.
Note: Always remember when capacitors are connected parallelly the the voltage across each capacitor will remain constant. Before calculating change, first change the capacitor and voltage to its SI unit to get the charge in coulomb because coulomb is voltage multiplied by farad.
Complete step by step answer:
(a) As per the problem there are three capacitors of capacitance $2pF,3pF$ and $4pF$are connected parallel. When capacitors are connected parallel to each other then their total resistance is calculated by adding all the capacitance.Now we can get,
Total capacitance = capacitance one + capacitance two + capacitance three
Mathematically,
$C = {C_1} + {C_2} + {C_3} \ldots \ldots \left( 1 \right)$
Given,
${C_1} = 2pF$
$\Rightarrow {C_2} = 3pF$
$\Rightarrow {C_3} = 4pF$
Here $pF$ is the unit of capacitance.
PicoFarad = pF
Hence total capacitance,
Putting the given values in equation $\left( 1 \right)$ we get,
$C = 2pF + 3pF + 4pF$
On further solving we get,
$\therefore C = 9\,pF$
Therefore the total capacitance of the combination is $9\,pF$.
(b) As we know the supply voltage to the capacitance is $100V$. Three capacitance is connected parallelly hence voltage will remain same for all the capacitor.We know,
$q = VC \ldots \ldots \left( 2 \right)$
Where, Charge of the capacitor = $q$, Supply Voltage or voltage across capacitor = $V$ and Capacitance = $C$.
Using equation $\left( 2 \right)$ in all the three cases:
For capacitor one we get,
${q_1} = V{C_1}$
Now putting the given values in the equation we get,
${q_1} = 100V \times 2pF$
We know,
$1pF = {10^{ - 12}}F$
Now the change become,
${q_1} = 100V \times 2 \times {10^{ - 12}}F$
$\Rightarrow {q_1} = 2 \times {10^{ - 10}}C$
Unit is coulomb.
Similarly, for charge two we get,
${q_2} = V{C_2}$
Now putting the given values in the equation we get,
${q_2} = 100V \times 3pF$
$ \Rightarrow {q_2} = 100V \times 3 \times {10^{ - 12}}F$
$ \Rightarrow {q_2} = 3 \times {10^{ - 10}}C$
For charge three we get,
${q_3} = V{C_3}$
Now putting the given values in the equation we get,
${q_3} = 100V \times 4pF$
$ \Rightarrow {q_3} = 100V \times 4 \times {10^{ - 12}}F$
$ \Rightarrow {q_3} = 4 \times {10^{ - 10}}C$
Hence, upon keeping the supply voltage to the all three capacitors at $100V$, we can observe only change in their charges as $2 \times {10^{ - 10}}C$, $3 \times {10^{ - 10}}C$ and $4 \times {10^{ - 10}}C$.
Note: Always remember when capacitors are connected parallelly the the voltage across each capacitor will remain constant. Before calculating change, first change the capacitor and voltage to its SI unit to get the charge in coulomb because coulomb is voltage multiplied by farad.
Recently Updated Pages
A man running at a speed 5 ms is viewed in the side class 12 physics CBSE

The number of solutions in x in 02pi for which sqrt class 12 maths CBSE

State and explain Hardy Weinbergs Principle class 12 biology CBSE

Write any two methods of preparation of phenol Give class 12 chemistry CBSE

Which of the following statements is wrong a Amnion class 12 biology CBSE

Differentiate between action potential and resting class 12 biology CBSE

Trending doubts
What are the major means of transport Explain each class 12 social science CBSE

Which are the Top 10 Largest Countries of the World?

Draw a labelled sketch of the human eye class 12 physics CBSE

How much time does it take to bleed after eating p class 12 biology CBSE

Explain sex determination in humans with line diag class 12 biology CBSE

When was the first election held in India a 194748 class 12 sst CBSE

