Questions On Equivalent Capacitance Class 12

Capacitance is a crucial topic in Class 12 physics, particularly in the study of electrostatics. Understanding equivalent capacitance is essential when dealing with capacitors in series and parallel. Many students struggle with calculating the total capacitance in a circuit, especially when facing complex combinations.

This topic will explore questions on equivalent capacitance, providing concepts, formulas, and solved examples to make the topic easier to grasp.

Table of Contents

What Is Equivalent Capacitance?

Equivalent capacitance is the total capacitance of a network of capacitors. When multiple capacitors are connected, their overall effect can be replaced by a single capacitor with the same charge storage ability. The calculation of equivalent capacitance depends on the type of connection:

Series connection
Parallel connection
Mixed combination (series + parallel)

Capacitors in Series

When capacitors are connected in series, the total capacitance is less than the smallest individual capacitor. The formula to calculate the equivalent capacitance is:

frac{1}{C_{text{eq}}} = frac{1}{C_1} + frac{1}{C_2} + frac{1}{C_3} + dots

Key points to remember:

The same charge flows through each capacitor.
The voltage divides among the capacitors.
The total capacitance is always smaller than the smallest capacitor in the series.

Example Question on Series Connection

Q: Three capacitors of 4 µF, 6 µF, and 12 µF are connected in series. What is the equivalent capacitance?

Solution:

Using the formula:

frac{1}{C_{text{eq}}} = frac{1}{4} + frac{1}{6} + frac{1}{12}

frac{1}{C_{text{eq}}} = frac{3}{12} + frac{2}{12} + frac{1}{12} = frac{6}{12} = frac{1}{2}

C_{text{eq}} = 2 text{ µF}

Thus, the equivalent capacitance is 2 µF.

Capacitors in Parallel

When capacitors are connected in parallel, the total capacitance is greater than the largest individual capacitor. The formula for calculating equivalent capacitance is:

C_{text{eq}} = C_1 + C_2 + C_3 + dots

Key points to remember:

The voltage across each capacitor is the same.
The charge gets divided among the capacitors.
The total capacitance is always greater than the largest capacitor in the parallel connection.

Example Question on Parallel Connection

Q: Three capacitors of 5 µF, 10 µF, and 20 µF are connected in parallel. What is the equivalent capacitance?

Solution:

Using the formula:

C_{text{eq}} = 5 + 10 + 20 = 35 text{ µF}

Thus, the equivalent capacitance is 35 µF.

Mixed Combinations of Capacitors

In real-life circuits, capacitors are often arranged in a combination of series and parallel. In such cases, break down the circuit into simpler parts by first calculating the series capacitance and then adding parallel capacitance.

Example Question on Mixed Combination

Q: Find the equivalent capacitance of the following arrangement:

A 4 µF and a 6 µF capacitor in series.
This combination is in parallel with a 3 µF capacitor.

Solution:

Step 1: Calculate series capacitance of 4 µF and 6 µF

frac{1}{C_{text{series}}} = frac{1}{4} + frac{1}{6}

frac{1}{C_{text{series}}} = frac{3}{12} + frac{2}{12} = frac{5}{12}

C_{text{series}} = frac{12}{5} = 2.4 text{ µF}

Step 2: Add the parallel capacitor (3 µF)

C_{text{eq}} = 2.4 + 3 = 5.4 text{ µF}

Thus, the total capacitance is 5.4 µF.

Important Questions for Practice

Three capacitors of 2 µF, 4 µF, and 8 µF are connected in series. What is the equivalent capacitance?
Two 10 µF capacitors are connected in parallel. Find the total capacitance.
A 6 µF capacitor is in series with a parallel combination of 3 µF and 6 µF. Calculate the equivalent capacitance.
Identify the equivalent capacitance when two capacitors of 5 µF and 10 µF are first connected in series, and the result is in parallel with a 15 µF capacitor.
Explain why the equivalent capacitance in a series combination is always less than the smallest capacitor in the series.

Common Mistakes Students Make

Confusing series and parallel formulas – Remember that series capacitance decreases, while parallel capacitance increases.
Not simplifying fractions correctly – When calculating series capacitance, always simplify fractions properly.
Ignoring units – The unit of capacitance is farads (F), but questions often use microfarads (µF), so pay attention to unit conversions.
Forgetting voltage distribution – In a series connection, voltage divides across capacitors, while in parallel, voltage remains the same.
Skipping verification – Always double-check answers to ensure logical consistency, especially for mixed connections.

Real-Life Applications of Equivalent Capacitance

Capacitors are widely used in electronic circuits. Understanding equivalent capacitance is essential for designing:

Power supply circuits – Capacitors help in filtering and voltage stabilization.
Tuned circuits – Used in radios and televisions for frequency selection.
Flash cameras – Capacitors store energy for sudden discharges in camera flashes.
Medical devices – Defibrillators use capacitors to deliver controlled electric shocks.

Equivalent capacitance is a fundamental concept in physics, essential for circuit analysis and real-world applications. Mastering the formulas for series and parallel combinations, along with practicing numerical problems, helps in achieving a solid understanding.

By avoiding common mistakes and understanding how capacitors interact in circuits, students can confidently solve Class 12 physics problems on equivalent capacitance and apply their knowledge effectively in practical situations.