A 2.0 μF capacitor and a 4.0μF capacitor are connected in parallel across a 300 V potential diff

Name: Problem 31, Chapter 25: Fundamentals of Physics
Uploaded: 2020-02-15T08:16:36-08:00
Duration: 46 s
Channel: Salamat Ali
Description: A 2.0 μF capacitor and a 4.0μF capacitor are connected in parallel across a 300 V potential difference. Calculate the total energy stored in the capacitors.

step 1 The total energy stored in two capacitors, which are connected parallel, is given by energy of 1

Question

$\mathrm{A} 2.0 \mu \mathrm{F}$ capacitor and a 4.0$\mu \mathrm{F}$ capacitor are connected in parallel across a 300 $\mathrm{V}$ potential difference. Calculate the total energy stored in the capacitors.

   $\mathrm{A} 2.0 \mu \mathrm{F}$ capacitor and a 4.0$\mu \mathrm{F}$ capacitor are connected
in parallel across a 300 $\mathrm{V}$ potential difference. Calculate the total
energy stored in the capacitors.

Fundamentals of Physics

David Halliday,… 10th Edition

Chapter 25, Problem 31

Instant Answer

Solved by Expert Salamat Ali

02/15/2020

Step 1

So, we can write: \[C = C_1 + C_2\] Substituting the given values, we get: \[C = 2 \times 10^{-6} F + 4 \times 10^{-6} F = 6 \times 10^{-6} F\] Show more…

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$\mathrm{A} 2.0 \mu \mathrm{F}$ capacitor and a 4.0$\mu \mathrm{F}$ capacitor are connected in parallel across a 300 $\mathrm{V}$ potential difference. Calculate the total energy stored in the capacitors.

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Key Concepts

Parallel Capacitor Connection

When capacitors are connected in parallel, they each experience the same voltage across their terminals. This configuration means that the total capacitance of the system is the sum of the individual capacitances, which simplifies the process of calculating overall energy storage or charge. Understanding parallel connections is fundamental when analyzing circuits where energy distribution across multiple capacitors is considered.

Energy Stored in a Capacitor

The energy stored in a capacitor is given by the formula U = ½ C V², where U is the energy, C is the capacitance, and V is the voltage across the capacitor. This formula highlights that the energy stored is directly proportional to both the capacitance and the square of the voltage. It is a key concept in understanding how capacitors function in storing and releasing electrical energy in various circuits.

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