Aparallel plate capacitor A is filled with a dielectric whose dielectr...
Introduction:
We are given two parallel plate capacitors, A and B. Capacitor A is filled with a dielectric whose dielectric constant varies with applied voltage as K-V, while capacitor B has air as its dielectric. Capacitor B is initially connected to a voltage source Vo-30V and then connected to capacitor A after disconnecting the voltage source. We need to determine the charge and voltage on capacitor A after the connection.
Explanation:
Step 1: Capacitor B connected to voltage source:
- Capacitor B is initially connected to a voltage source Vo-30V. This means that the voltage across capacitor B is Vo-30V.
- The capacitance of capacitor B is given as Co (given in the problem).
Step 2: Disconnecting the voltage source and connecting capacitor A:
- After disconnecting the voltage source, the voltage across capacitor B remains constant at Vo-30V.
- Capacitor B is now connected to capacitor A.
- When capacitors are connected in parallel, the voltage across them is the same.
- Therefore, the voltage across capacitor A is also Vo-30V.
Step 3: Calculation of charge on capacitor A:
- The charge on a capacitor is given by the equation Q = CV, where Q is the charge, C is the capacitance, and V is the voltage.
- The capacitance of capacitor B is Co (given in the problem).
- The capacitance of capacitor A can be calculated using the equation C = K * Co, where K is the dielectric constant.
- Since the dielectric constant varies with applied voltage as K-V, the capacitance of capacitor A also varies with voltage.
- Let's assume the capacitance of capacitor A at the given voltage (Vo-30V) is C'.
- Therefore, the charge on capacitor A can be calculated as Q' = C' * (Vo-30V).
Step 4: Final values of charge and voltage on capacitor A:
- After the connection, the charge on capacitor A is Q' and the voltage across it is Vo-30V.
Conclusion:
- The charge on capacitor A after connecting it to capacitor B is given by Q' = C' * (Vo-30V), where C' is the capacitance of capacitor A at the given voltage (Vo-30V).
- The voltage across capacitor A after the connection is Vo-30V.
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