Finding unknown capacitor in complex network

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

First I calculated equivalent capacitance between R and M . The two 2μF capacitors are in series . Their combination is in parallel with the 1μF capacitor . Their equivalent capacitance is 2μF .

Now I found equivalent capacitance between R and T .The previously calculated 2μF between R and M is in series with 8μF capacitor .The equivalent capacitance between R and T is 8/5 μF.

Now I found equivalent capacitance between P and Q . Using nodal analysis I found it to be 44/3 μF .

The net capacitance between P and Q i.e 44/3 μF and net capacitance between R and T i.e 8/5 μF are in parallel . So, net capacitance between P and T is 244/15 μF .

Across A and B this 244/15 μF is in series with the unknown capacitor C . Their net capacitance has to be 3μF . Calculations give me value of C =732/199 μF . This is incorrect .

What is the mistake ?

 

[cnh1995]

Now I found equivalent capacitance between P and Q . Using nodal analysis I found it to be 44/3 μF .

You can use delta-star transformation for that. It's quicker.

 

[ehild]

Homework Statement

View attachment 221625

Homework Equations

The Attempt at a Solution

First I calculated equivalent capacitance between R and M . The two 2μF capacitors are in series . Their combination is in parallel with the 1μF capacitor . Their equivalent capacitance is 2μF .

Now I found equivalent capacitance between R and T .The previously calculated 2μF between R and M is in series with 8μF capacitor .The equivalent capacitance between R and T is 8/5 μF.

Now I found equivalent capacitance between P and Q . Using nodal analysis I found it to be 44/3 μF .

The net capacitance between P and Q i.e 44/3 μF and net capacitance between R and T i.e 8/5 μF are in parallel . So, net capacitance between P and T is 244/15 μF .

Across A and B this 244/15 μF is in series with the unknown capacitor C . Their net capacitance has to be 3μF . Calculations give me value of C =732/199 μF . This is incorrect .

What is the mistake ?

Your solution is correct. Try to give C = 3.68 μF.
The capacitance between P and Q is easy to calculate with parallel and series capacitors. The 2μF and 6μF capacitors are parallel, connected in series with the 4 μF capacitor, and the whole in parallel with the 12 μF capacitor.

 

[Jahnavi]

The capacitance between P and Q is easy to calculate with parallel and series capacitors. The 2μF and 6μF capacitors are parallel, connected in series with the 4 μF capacitor, and the whole in parallel with the 12 μF capacitor

Wow ! This is so nice .

I couldn't make out that it could be simplified in this way .

For me , the difficult part in this question was finding capacitance between P and Q . You made it look so easy

 

[Jahnavi]

Your solution is correct. Try to give C = 3.68 μF.

This is a previous year exam question . But the circuit in the question is actually wrong . This is why I was not getting the correct answer 48 μF

The original question is given below .

As you can see there is an extra wire in the picture in the OP .