Five capacitors are connected across a potential difference V ab as shown in Fig

Question

Five capacitors are connected across a potential difference Vab as shown in Figure. Because of the dielectrics used, each capacitor will break down if the potential across it is V=23 V. What should be the value of Vab(with one decimal place) if you reach the break down voltage one of the capacitor.

Five capacitors are connected across a potential difference Vab as shown in Figure. Because of the dielectrics used, each capacitor will break down if the potential across it is V=23 V. What should be the value of Vab (with one decimal place) if you reach the break down voltage one of the capacitor.

Explanation / Answer

Let's assume that all the capacitors don't have a value. Starting from the top left corner, in a clockwise direction, we have C1, C2, C3, C4, and C5.

Since they are all inline, the inverse of each capacitance added together is equal to the inverse of the total capacitance. Therefore, 1/C1 + 1/C2 + 1/C3 + 1/C4 + 1/C5 = 1/Ctotal

Just add all of them in your calculator and you'll get a really huge number. That number is equal to 1/Ctotal, so take the inverse to get the total capacitance of the circuit.

Ctotal * Vab = Qtotal

Since the capacitors are inline, the charge Q for each individual capacitor is the same as the charge for the whole system, Qtotal.

So, choosing a capacitor C at random(You can choose any of the five), you get the equation C = Qtotal / Vc

Vc is equal to the voltage going through that individual capacitor, which varies depending on the strength of the capacitor. The problem says that if the voltage in any capacitor exceeds 23 volts it will break down, therefore you must assume that the voltage traveling through C can't exceed 23. That means Vc must equal 23.

Now, we have C = (Ctotal * Vab) / Vc

Since Ctotal and Vc are constant values, this means that Vab is dependent on C. Soooo, to get the maximum allowed voltage without breaking the system, you have to find which capacitor C yields the smallest voltage Vab.

Just for reference:

If we manipulate the equation, we get Vc = (Ctotal * Vab) / C

Since Vc is a constant, each C value gives a different Vab from the above equation, but only one Vab will give you Vc<23 for every value C

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