A 10uf is connected to a 300v PD and isolated. it is then connected in parallel to 5uf ,find the resultant pd.the energy stored before connection and energy in two capacitor after connection
To find the resultant potential difference (PD) when a 10μF capacitor is connected in parallel to a 5μF capacitor, we can use the concept of charge conservation. Before connection, the 10μF capacitor is connected to a 300V potential difference (PD) in isolation.
The charge on the 10μF capacitor can be calculated using the formula:
Q = C × V
Where Q is the charge, C is the capacitance, and V is the potential difference.
For the 10μF capacitor:
Q₁ = 10μF × 300V
Q₁ = 3,000μC
Now, when the 10μF capacitor is connected in parallel to the 5μF capacitor, the total charge remains the same. Therefore, the charge on both capacitors after connection will also be 3,000μC.
To find the resultant potential difference, we can use the formula:
V = Q / C
For the 5μF capacitor:
V₂ = Q / 5μF
V₂ = 3,000μC / 5μF
V₂ = 600V
Therefore, the resultant potential difference across the combination of the capacitors will be 600V.
Now, let's calculate the energy stored before connection and the energy in each capacitor after connection.
The energy stored in a capacitor can be calculated using the formula:
E = 1/2 × C × V²
Energy stored before connection:
E₁ = 1/2 × 10μF × (300V)²
E₁ = 45mJ
Energy stored in the 10μF capacitor after connection:
E₂ = 1/2 × 10μF × (600V)²
E₂ = 180mJ
Energy stored in the 5μF capacitor after connection:
E₃ = 1/2 × 5μF × (600V)²
E₃ = 90mJ
Therefore, the energy stored in the 10μF capacitor after connection is 180mJ, and the energy stored in the 5μF capacitor after connection is 90mJ.