Finding the potential across capacitors in capacitor-only circuits

Gourab_chill · Apr 5, 2020

I tried to attempt it by applying KVL to both the loops.

Circuit schematic of two loops sharing branch MN, with capacitors C1 and C2 and two batteries of emf E; charges Q, -Q, Q1, -Q1 and -(Q - Q1) labelled on the plates, with loop arrows (1) and (2).

I tried to find a possible charge distribution for the capacitors. I guess this is right.

Two typed equations. First: E = ((Q − Q1)/C1) − Q1/C2. Second: E = Q/C2 − Q1/C2.

On solving I get:

$Handwritten-style equation: Q1 = E C2 (C2 - C1) / C1, with Q1 on the left and the fraction bar over C1.$

from what I know potential difference between M and N is Q1/C2
but the solution is given as:

$Equation V_MN = |E((C2 - C1)/(2C2 + C1))|, with V_MN on the left and an absolute value bar enclosing E times the fraction (C2 minus C1) over (2C2 plus C1).$

Where am I wrong?

TSny · Apr 5, 2020

Welcome to PF!

You have a sign error in one of your first two equations.

Gourab_chill · Apr 7, 2020

TSny said:

Welcome to PF!

You have a sign error in one of your first two equations.

thanks

Finding the potential across capacitors in capacitor-only circuits

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