# 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...........

Arun
25757 Points
3 years ago
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Arun
Khimraj
3007 Points
3 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 !