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Two capacitors have capacitances in the ratio 2 : 3. They are connected in parallel in a circuit. The energy stored in the capacitors are in the ratio?
- a)1 : 2
- b)2 : 3
- c)3 : 2
- d)1 : 3
Correct answer is option 'B'. Can you explain this answer?
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Two capacitors have capacitances in the ratio 2 : 3. They are connecte...
Parallel connection means V1 = V2
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Two capacitors have capacitances in the ratio 2 : 3. They are connecte...
Solution:
Given, the capacitances of two capacitors are in the ratio of 2:3.
Let the capacitances of the capacitors be 2x and 3x respectively.
When capacitors are connected in parallel, the equivalent capacitance is given by
C = C₁ + C₂
C = 2x + 3x
C = 5x
Hence, the equivalent capacitance is 5x.
The energy stored in a capacitor is given by the formula:
U = 1/2 CV²
where U is the energy stored, C is the capacitance and V is the voltage across the capacitor.
Let the voltage across the capacitors be V.
The energy stored in the first capacitor is given by
U₁ = 1/2 (2x)V²
U₁ = xV²
The energy stored in the second capacitor is given by
U₂ = 1/2 (3x)V²
U₂ = 3/2 xV²
The total energy stored in the capacitors is given by
U = U₁ + U₂
U = xV² + 3/2 xV²
U = 5/2 xV²
Therefore, the energy stored in the capacitors is in the ratio of 1:3.
Hence, the correct option is (B) 2:3.
Given, the capacitances of two capacitors are in the ratio of 2:3.
Let the capacitances of the capacitors be 2x and 3x respectively.
When capacitors are connected in parallel, the equivalent capacitance is given by
C = C₁ + C₂
C = 2x + 3x
C = 5x
Hence, the equivalent capacitance is 5x.
The energy stored in a capacitor is given by the formula:
U = 1/2 CV²
where U is the energy stored, C is the capacitance and V is the voltage across the capacitor.
Let the voltage across the capacitors be V.
The energy stored in the first capacitor is given by
U₁ = 1/2 (2x)V²
U₁ = xV²
The energy stored in the second capacitor is given by
U₂ = 1/2 (3x)V²
U₂ = 3/2 xV²
The total energy stored in the capacitors is given by
U = U₁ + U₂
U = xV² + 3/2 xV²
U = 5/2 xV²
Therefore, the energy stored in the capacitors is in the ratio of 1:3.
Hence, the correct option is (B) 2:3.
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Two capacitors have capacitances in the ratio 2 : 3. They are connected in parallel in a circuit. The energy stored in the capacitors are in the ratio?a)1 : 2b)2 : 3c)3 : 2d)1 : 3Correct answer is option 'B'. Can you explain this answer?
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