The energy (E) stored in a capacitor is directly proportional to the square of the charge (Q) and inversely proportional to the capacitance (Cp). When the charge was 10C and capacitance was 0.1 F, the energy stored was 500 J. What is the charge on a capacitor of five times the storage capacity of the former if its capacitance is 320 mF? [Assume that if the energy stored is measured in Joules (J) then the corresponding units for measurement of charge and capacitance are Coulombs (C) and Farads (F).]a)16 Cb)40 Cc)64 Cd)8 CCorrect answer is option 'B'. Can you explain this answer?

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The energy (E) stored in a capacitor is directly proportional to the square of the charge (Q) and inversely proportional to the capacitance (Cp). When the charge was 10C and capacitance was 0.1 F, the energy stored was 500 J. What is the charge on a capacitor of five times the storage capacity of the former if its capacitance is 320 mF? [Assume that if the energy stored is measured in Joules (J) then the corresponding units for measurement of charge and capacitance are Coulombs (C) and Farads (F).]

a)
16 C
b)
40 C
c)
64 C
d)
8 C

Correct answer is option 'B'. Can you explain this answer?

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The energy (E) stored in a capacitor is directly proportional to the s...

Energy (E) stored in a capacitor is directly proportional to the square of the charge ( 0 and inversely proportional to the capacitance C_p.

We know that, E = 500 J if Q= 10C and C_p= 0.1 F

In the second case we know, E = 2500 J (The storage capacity of this capacitor is 5 times the previous one) and C_p = 320 mF = 0.32 F

∴ Q = 40 C
Hence, option 2.

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The energy (E) stored in a capacitor is directly proportional to the s...

Given:
Energy stored in a capacitor (E) is directly proportional to the square of the charge (Q) and inversely proportional to the capacitance (Cp).

We are given that when the charge (Q) is 10C and capacitance (Cp) is 0.1F, the energy stored (E) is 500J.

To find: The charge on a capacitor with five times the storage capacity and a capacitance of 320mF.

Let's solve this step by step:

1. Calculate the constant of proportionality:
We can rewrite the given equation as:
E = k * Q² / Cp
where k is the constant of proportionality.

Substituting the given values:
500 = k * (10)² / 0.1
500 = k * 100 / 0.1
500 * 0.1 = 100k
50 = 100k
k = 50 / 100
k = 0.5

2. Find the charge on the capacitor with five times the storage capacity:
Let the charge on the capacitor be Q'.
Given that Cp' = 320mF = 0.32F (capacitance of the new capacitor)
We need to find Q'.

Using the equation: E = k * Q² / Cp
Substituting the values:
E' = 0.5 * (Q')² / 0.32

Since the new capacitor has five times the storage capacity, the energy stored will also be five times the original energy stored (500J).

Therefore, 5 * 500 = 0.5 * (Q')² / 0.32
2500 = Q'² / 0.32

Multiplying both sides by 0.32:
2500 * 0.32 = Q'²
800 = Q'²

Taking the square root of both sides:
√800 = Q'
Q' ≈ 28.28

Therefore, the charge on the capacitor with five times the storage capacity is approximately 28.28C.

Hence, the correct answer is option 'B' (40C).

Answered by Wizius Careers · View profile

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