when two capacitors are connected in series, the effective capacitance is 2 4 micro farad and when connected in parallel, - Physics - Electrostatic Potential And Capacitance

Question

when two capacitors are connected in series, the effective
capacitance is 2 4 micro farad and when connected in parallel, the
effective capacitance is 10 micro farad calculate the individual
capacitances

Aditi · Accepted Answer

When two capacitors are connected in series then total capacitance
i e C is
1/C= 1/C1+1/C2
where,
C1 is the capacitance of 1st capacitor
C2 is the capacitance of 2nd capacitor
Given,
C = 2 4 micro farad
1/2 4 = 1/C1+1/C2
C1× C2 = 2 4 C1 + 2 4
C2 (1)

Now if capacitors are connected in parallel,then total capacitance
is i e C
C= C1+C2
given, C = 10 micro farad
10 = C1+ C2 (2)
Now, from 1st and 2nd equation,
C1×C2 = 24
i e C1 = 24/C2 (3)
now substitute value of C1 in equation
2nd,
We get,
C12 -10 C1 +24 = 0
â‡¨ C1 = 6 or 4
also from 3rd equation, C2 = 4 or 6

when two capacitors are connected in series, the effective capacitance is 2.4 micro farad and when connected in parallel, the effective capacitance is 10 micro farad. calculate the individual capacitances.