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two capacitors of unknown capacitance c1 and c2 arew connected first in series and tnen in parallel across 100 v battery if the energy stored in two capacitor...........

two capacitors of unknown capacitance c1 and c2 arew connected first in series and tnen in parallel across 100 v battery if the energy stored in two capacitor...........

Grade:12

2 Answers

Arun
25763 Points
2 years ago
Dear student
 
Question is incomplete. Please check and rrpost this. You can also attach an image. I will be happy to help you.
 
Regards
Arun
Khimraj
3007 Points
2 years ago
Energy stored in a capacitor
                                 E = 1/2CV²
In series combination 
    0.045 = 1/2 C₁C₂/2C₁ + C₂ (100)²
→ C₁C₂/C₁ + C₂ = 0.09 × 10⁻⁴  -------------> (1)
In parallel combination 
       0.25 = (C₁ + C₂) (100)²
→ C₁ + C₂ = 0.5 × 10⁻⁴  ----------------------> (2)
On simplifying (1) and (2)
    C₁C₂ = 0.045 × 10⁻⁸
 
 (C₁ - C₂)²= ( C₁ + C₂)² - 4C₁C₂
            = (0.5 × 10⁻⁴) - 4 × 0.045 × 10⁻⁸
            = 0.25 × 10⁻⁸ - 0.180 × 10⁻⁸
(C₁ - C₂)² = 0.07 × 10⁻⁸
(C₁ - C₂)² = 2.6 × 10⁻⁵ = 0.25 × 10⁻⁴ -------------------> (3)
 Now, 
From (2) and (3)
C₁ = 0.38 × 10⁻⁴ F and C₂ = 0.12 × 10⁻⁴ F
Charges on capacitors C₁ and C₂ in parallel combination 
Q₁ = C₁V = (0.38 × 10⁻⁴ × 100) = 0.38 × 10⁻² C
Q₂ = C₂V = (0.12 ×10⁻⁴ × 100) = 0.12 × 10⁻² C

Hope it helps you !
 

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