Question

(a)Derive an expression for the energy stored in a parallel plate capacitor.

(b) A network of four 10 uF capacitors are connected to a 500V supply as shown in the figure. Determine the (i) equivalent capacitance of
the network and (ii) charge on each capacitor.
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Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

(a)The energy stored on a capacitor is based on the work done by the battery in the circuit. The battery voltage represent the energy per unit charge. Hence, the work done to move a charge element dq from the negative plate to the positive plate is equal to V dq.

(b)Explanation:

Given that,

The value of each capacitors = 12μF

Voltage = 500 V

According to figure,

C₁, C₂ and C₃ are connected in series

We need to calculate the equivalent capacitance

Using formula of series

Put the value into the formula

Now, C and C₄ is connecting in parallel

We need to calculate the equivalent capacitance

Using formula for parallel

Put the value into the formula

We need to calculate the charge C₁, C₂ and C₃

Using formula of charge

Put the value in to the formula

We need to calculate the voltage across parallel capacitors

Using formula of voltage

Put the value into the formula

We need to calculate the across voltage on C₄

We need to calculate the charge on C₄

Using formula of charge

Hence, The equivalent capacitance is 16 μF.

The charge on C₁, C₂ , C₃ capacitor and C₄ is   and

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