Question

The equivalent capacitance of two capacitors when joined in parallel is 16 µF and when joined in series is 3µF. The capacitance of the capacitors are..​

Answer 1

Answer:

12 muF , 16 muF

Explanation:

let the capacitance of capacitors be C1 and C2

for parallel combination C= C1+C2

=> C1+C2 = 16 ...........(1)

for series combination 1/C = 1/C1+1/C2

=> 1/C1+1/C2 = 1/3

=> (C1+C2)/C1C2 = 1/3

=> 16/C1C2 = 1/3 putting the value of C1+C2

=> C1C2 = 48

=> C1 = 48/C2.............(2)

solving (1) and (2)

C1 = 12 microF

C2= 4 microF

hope this helps you

Answer 2

Answer:

The capacitance of the capacitors is 4μF and 12μF respectively.

Explanation:

CASE I: When the capacitors are joined in parallel

$\mathrm{C_P=C_1+C_2}$           (1)

Where,

$\mathrm{C_P}$=equivalent capacitance of the capacitors when connected in parallel

C₁, C₂=individual capacitance of the capacitors

From the question we have,

The equivalent capacitance of the capacitors when joined in parallel=16μF=16×10⁻⁶F

Inserting the value of "$\mathrm{C_P}$" in equation (1) we get;

$\mathrm{16\times 10^{-6}=C_1+C_2 }$             (2)

$\mathrm{C_1=16\times 10^{-6} -C_2 }$             (3)

CASE II: When the capacitors are joined in series

$\mathrm{C_s=\frac{C_1C_2}{C_1+C_2} }$                (4)

Where,

$\mathrm{C_s}$=equivalent capacitance of the capacitors when connected in parallel

C₁, C₂=individual capacitance of the capacitors

From the question we have,

The equivalent capacitance of the capacitors when joined in series=3μF=3×10⁻⁶F

Inserting the value of "$\mathrm{C_s}$" in equation (4) we get;

$\mathrm{3\times 10^{-6}=\frac{C_1C_2}{C_1+C_2} }$      (5)

Now using equation (2) in equation (5) we get;

$\mathrm{3\times 10^{-6}=\frac{C_1C_2}{16\times 10^{-6}} }}$    

$\mathrm{C_1C_2=48\times 10^{-12}}$  (6)

Using equation (3) in equation (6) we get;

$\mathrm{(16 -C_2)C_2=48}$

$\mathrm{16C_2 -C_2^2=48}$

$\mathrm{C_2^2+48-16C_2=0}$

$\mathrm{(C_2-12)(C_2-4)=0}$

$\mathrm{C_2=4,12\ \mu F}$        (7)

So, the capacitance of the capacitors is 4μF and 12μF respectively.

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