Question

Is connecting capacitors in parallel more similar to connecting two resistors in parallel or connecting two batteries in parallel? Explain thouroughly please.

Answer 1

To answer this question we need to check the parallel combiation of capacitor, resistor, and batteries, what happen to their effective value.

Two Batteries in Parallel

Consider two cells which is connected in parallel. Here the positive terminals of all cells are connected together and negative terminals of all cells are connected together. In parallel connection, the current is divided among the braches. Thus, the current I is split into I1 and I2. I = I1 + I2.  Consider the points B1 and B2 and then V (B1) and V (B2) are the potentials respectively. The potential difference across the terminals of the first cell.

V = V (B1) - V (B2) = ε1- I1 r1. The point B1 and B2  are connected similar to the second cell.

V = V (B1) - V (B2) = ε2 – I2 r2. By ohm’s law we know that I = V / R. Now substitute these values in the equation

If we replace the cells by a single cell lying between the point B1 and B2 with emf εeq  and internal resistance req, then V = εeq - Ireq.

It is the same as when we connect the resistors in parallel connection.

For n number of cells connected in parallel with emf ε1, ε2…… εn  and internal resistance r1, r2…. rn

So for two bateries and taking internal resistance as unity, weca have

E_eg=E₁+E₂

So in parallel conection the batteries adds up.

Two Reistor in Parallel

Two Capacitor in Parallel Connection

So from above three cases it's clear that in parallel connection only batteries and capacitors algebrically adds up, so conectiong capacitor in parallel is more similar to connecting two batteries in parallel.