Question

Three capacitors of 10muF, 25muF, and 50 muF are connected in series. Each capacitor is rated for 24V operation. is it safe to apply a total of 24V x 3=72 across their combination? If not safe, what is the maximum voltage that can be supplied across their combination so that the voltage drops across any of the three capacitors will not exceed their rated voltage of 24V?

Answer 1

Given that three capacitors are connected in series, So

1/Ceq = 1/C1 + 1/C2 + 1/C3

Ceq = (1/10 + 1/25 + 1/50)^-1

Ceq = 6.25 F

Now given that each capacitor is rated for 24 V, So when 72 V is applied across their combination, then total charge across circuit will be:

Qeq = Ceq*V

Qeq = 6.25*72 = 450 C

Now remember in capacitors parallel combination voltage distribution in each part will be same and in series combination charge distribution in each capacitor will be same, Since all three are connected in series, So charge flow through each will be same

Q1 = Q2 = Q3 = 450 C

Now potential drop across C1 will be:

V1 = Q1/C1 = 450 C/10 F = 45 V

V2 = Q2/C2 = 450 C/25 F = 18 V

V3 = Q3/C3 = 450 C/50 F = 9 V

Since capacitors are rated for 24 V operation, So it will not be safe for C1 to operate at this voltage.

Now we know that max potential drop will be across C1, since that capacitor has lowest capacitance, So assuming Voltage drop across C1 is 24 V, then in that case

Q1 = C1*V1 = 10 F*24 V = 240 C

And since all three in series, So for this same charge potential drop across C2 and C3 will be:

V2 = Q2/C2 = 240 C/25 F = 9.6 V

V3 = Q3/C3 = 240 C/50 F = 4.8 V

So max voltage that can be applied, So that voltage drops across any of the three capacitors will not exceed their rated voltage of 24V, will be:

V = V1 + V2 + V3 = 24 + 9.6 + 4.8

V = 38.4 V

Let me know if you've any query.