Effective capacitance of parallel combination of two capacitors C1 and C2 is 10 μ F. When these capacitors are individually connected to a voltage source of 1 V , the energy stored in the capacitor C2 is 4 times that of C1. If these capacitors are connected in series, their effective capacitance will be :

Question

Effective capacitance of parallel combination of two capacitors C1 and C2 is 10 μ F. When these capacitors are individually connected to a voltage source of 1 V , the energy stored in the capacitor C2 is 4 times that of C1. If these capacitors are connected in series, their effective capacitance will be : (A) 1.6 μ F (B) 8.4 μF (C) 3.2 μF (D) 4.2 μF

Tardigrade Admin · Accepted Answer

C1+C2=10...(i) (1/2)C2V2=4×(1/2)C1V2 ∴ C2=4C1 ∴ C1=2 C2=8 For series combination Ceq=(C1C2/C1+C2)=1.6

1.6 $μ F$

8.4 $μ$ F

3.2 $μ$ F

4.2 $μ$ F

$C_{1} + C_{2} = 10... (i)$
$\frac{1}{2} C_{2} V^{2} = 4 \times \frac{1}{2} C_{1} V^{2}$
$∴ C_{2} = 4 C_{1}$
$∴ C_{1} = 2 & C_{2} = 8$
For series combination
$C_{e q} = \frac{C _{1} C _{2}}{C _{1} + C _{2}} = 1.6$

1.6 μF

8.4 μF

3.2 μF

4.2 μF

C1​+C2​=10...(i) 21​C2​V2=4×21​C1​V2 ∴C2​=4C1​ ∴C1​=2&C2​=8 For series combination Ceq​=C1​+C2​C1​C2​​=1.6

1.6 $μ F$

8.4 $μ$ F

3.2 $μ$ F

4.2 $μ$ F

$C_{1} + C_{2} = 10... (i)$
$\frac{1}{2} C_{2} V^{2} = 4 \times \frac{1}{2} C_{1} V^{2}$
$∴ C_{2} = 4 C_{1}$
$∴ C_{1} = 2 & C_{2} = 8$
For series combination
$C_{e q} = \frac{C _{1} C _{2}}{C _{1} + C _{2}} = 1.6$