Combination Of Capacitors

Step 1: Formula
Net capacitance for dielectrics in series: .
Step 2: Values
and .
Step 3: Calculation
.
Final Answer: (d)

Step 1: Apply the principle of conservation of charge.
When capacitors are connected in parallel, the total charge before and after connection is conserved. Initially, the charge on the 10 F capacitor is .

Step 2: Set up the equation.
After connection, the total charge is shared by both capacitors. The final potential difference across both capacitors is 20 V. Let be the capacitance of the second capacitor, then: Substitute the known values:

Step 3: Conclusion.
The capacitance of the second capacitor is 15 µF, which is option (4).

Step 1: Understanding the Concept:
Time period of simple pendulum: . Independent of mass.
Step 2: Detailed Explanation:
. New length .
.
Mass does not affect time period.
Step 3: Final Answer:
Thus, new time period = 3T.

Concept:
• Capacitors in series:
• Capacitors in parallel:

Step 1: Identify structure.
The circuit forms a bridge-like symmetric network.

Step 2: Use symmetry.
Due to symmetry, the potential at middle junctions becomes equal. Hence, no charge flows through the central bridge capacitor.

Step 3: Simplify circuit.
The network reduces to simple series-parallel combination:
• Left two capacitors combine
• Right two capacitors combine

Step 4: Final reduction.
After simplification:

Concept: For series capacitors: Charge is same on each capacitor:

Step 1: Equivalent capacitance.


Step 2: Charge.

Concept:
•Capacitors in parallel:
•Capacitors in series:
•Same charge flows in series

Step 1:Combine parallel capacitors:

Step 2:Now in series with :

Step 3:Total charge:

Step 4:Voltage across :