Capacitors And Capacitance

We know that in steady state the capacitor behaves like as an open circuit i.e., capacitor will not pass the current.

So, the potential difference across the capacitor

Hence, the final charge on the capacitor is

Here,

or
or

Concept: Physics (Electrostatics) - Combinations of Capacitors.

Step 1: Recall the formulas for capacitor combinations.
• For identical capacitors connected in series, the equivalent capacitance is .
• For identical capacitors connected in parallel, the equivalent capacitance is .

Step 2: Evaluate the specific combination for Option A. For 5 capacitors in parallel, . If this combination is then placed in series with 2 more capacitors, the net capacitance is found by: $ $

The energy stored in a capacitor is given by the formula: where: - is the capacitance of the capacitor (in farads),
- is the voltage across the capacitor (in volts),
- is the energy stored in the capacitor (in joules).
Given the values for capacitance and voltage , you can directly substitute them into the formula to calculate the energy stored in the capacitor.

Concept: The energy stored in a capacitor is given by where
• = capacitance
• = potential difference
• = stored energy

Step 1: Convert the capacitance into SI units.

Step 2: Substitute the values into the formula.

Step 3: Simplify the expression. Thus the energy stored is

Concept: The energy stored in a capacitor is given by where
• = capacitance
• = potential difference

Step 1: Convert capacitance into SI unit.

Step 2: Substitute into the formula.

Step 3: Simplify the expression.

Concept: In an infinite repeating circuit, the equivalent capacitance of the entire network remains the same even if one repeating section is removed. Let the equivalent capacitance of the whole circuit be .

Step 1: Use the self-similar property of the infinite circuit. Because the circuit repeats infinitely, removing the first section leaves the same equivalent capacitance . Thus, the circuit effectively becomes a capacitor in series with capacitance .

Step 2: Solve the equation. Subtract from both sides: This shows that the repeating network behaves the same as a single capacitor .

Step 3: Determine the equivalent capacitance. Thus, the equivalent capacitance of the infinite circuit is