0
\$\begingroup\$

What is the equivalent capacitance when a capacitor is connected in parallel with a conducting wire?

For example something like this circuit: enter image description here

Suppose each capacitor has a capacitance 1 microfarad.We can easily notice the vertical axis of symmetry.Hence we can isolate the central junction.

I'm getting the equivalent capacitance of upper branch as as 3/8 microfarad using formula for capacitors in series i.e. 1/(1/1+1/1.5+1/1) microfarad .Therefore capacitance of the whole circuit is 3/8+3/8+0=3/4 microfarad.

However according to my textbook the answer is 2 microfarad.Where am I going wrong?

\$\endgroup\$
3
  • 1
    \$\begingroup\$ In reference to the second schematic you drew, the wire in the middle is a dead short. Those capacitors may as well not be in circuit from an electrical perspective... \$\endgroup\$
    – vicatcu
    Aug 29, 2016 at 2:17
  • \$\begingroup\$ So you mean capacitance is 0 ? @vicatcu \$\endgroup\$
    – user72436
    Aug 29, 2016 at 2:26
  • \$\begingroup\$ Did your schematic come out correctly? It doesn't look like it's a correct re-drawing of the original circuit. \$\endgroup\$ Aug 29, 2016 at 2:59

1 Answer 1

3
\$\begingroup\$

The top half of your circuit does nothing because it's shorted in the middle. The bottom half is 1 capacitor in parallel with a series connection of two groups of two capacitors in parallel.

Resulting capacitance = 1uF // ( 1uF//1uF + 1uF//1uF ) = 2uF

Your text is correct.

\$\endgroup\$
0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy