Combination Of Capacitors

Let the capacitance of capacitor be .
Thus capacitance of capacitor is .
Potential across the capacitor

Step 1: Understanding the Capacitor Circuit.
In this circuit, capacitors and are in series and their equivalent capacitance is: This series combination is in parallel with . The total equivalent capacitance of the circuit is: Step 2: Voltage Across .
The voltage across is given by the voltage division rule: Step 3: Final Answer.
Thus, the voltage across is .

Step 1: Structure of suspended type galvanometer.
In a suspended type moving coil galvanometer, the coil is suspended by a thin fibre and is free to rotate when current flows through it.

Step 2: Role of magnet.
The permanent magnet provides a strong radial magnetic field and remains fixed in position.

Step 3: Deflection mechanism.
When current passes through the suspended coil, it experiences a torque and rotates, producing deflection. The magnet itself does not move.

Step 4: Conclusion.
Thus, in a suspended type moving coil galvanometer, the magnet is stationary.

Step 1: Understanding the behavior of capacitors in series.
When capacitors are connected in series, the total capacitance is given by: For and , we have: Step 2: Voltage division across capacitors.
The voltage across each capacitor in a series combination is inversely proportional to its capacitance. Therefore, the ratio of the potential across to that across is given by: Substituting the values of and : Step 3: Conclusion.
Thus, the ratio of the potential across to that across is 4:1, which corresponds to option (D).

Concept: For an infinite repeating network, the equivalent capacitance of the entire circuit remains the same even after removing the first repeating section. This self-similarity allows us to form an equation for the equivalent capacitance. Let the equivalent capacitance between points and be .
Step 1: {Represent the infinite network using self-similarity.} After the first section, the remaining infinite network still has equivalent capacitance . The first section consists of:

• One capacitor in series along the top branch
• A vertical capacitor connected to the remaining network

Step 2: {Combine the vertical capacitor with the remaining network.} The vertical capacitor is in parallel with the equivalent capacitance of the remaining infinite network. Thus,
Step 3: {Find equivalent capacitance of the series combination.} The series combination of and is Substitute :
Step 4: {Solve the equation.} Dividing by :
Step 5: {Solve the quadratic equation.} Thus, Hence, the correct option is (B).