capacitance series

Question

Initially, a single capacitance C1 is wired to a battery. Then capacitance

C2 is added in series Are (a) the potential difference

across C1 and (b) the charge q1 on C1 now more than, less than, or

the same as previously? (c) Is the equivalent capacitance C12 of C1

and C2 more than, less than, or equal to C1? (d) Is the charge stored

on C1 and C2 together more than, less than, or equal to the charge

stored previously on C1?

Answer 1

Hi Dorsa R.,

Here's how you might think of a capacitor. It sits in the circuit, and builds up charge, until it generates a back-voltage exactly equal to the voltage of the battery. Then, no further current flows into/across it (I say into/across, b/c as it charges up, there's a little bit of current that flows through the circuit to do that). So, if you connect an additional capacitor in series, the two capacitors will share the pieces of the battery voltage between them, since acting together (which means, in series for capacitors) they generate a combined back-voltage to stop further current flow. How to visualize that process, so that you can immediately re-create the necessary equations? Well, the current that flows in the wire connecting the two capacitors is a single value. But the back-voltage generated in each capacitor is inversely related the individual capacitor's capacitance; that is, a given bit of charge will get soaked up in a high-capacitance capacitor, without generating much back-voltage.

Now, let's get to the specific questions: (a) the potential difference (voltage across) C1 has decreased; (b) the charge therefore has also decreased on C1, (c) the equivalent capacitance C12 hasn't changed, since the battery voltage is being spread across more capacitance, but with exactly proportional lower voltages on each capacitor, (d) the total charge is unchanged.

I might point out that this is way different than having the capacitors in parallel; then each one soaks up charge sufficient to generate the battery voltage as a back-voltage. AND, resistors are exactly the reverse situation to capacitors, in how they behave in series vs. parallel connections in circuits.

-- Cheers, --Mr. d.