Chapter 26: Q. 58 (page 740)

What are the charge on and the potential difference across each capacitor in FIGURE $P 26.58$ ?

Short Answer

Expert verified

The charge on each capacitor is $q_{1} = 45 μ C, q_{2} = q_{3} = 21.6 μ C$ respectively, and the potential difference across each capacitor is $U_{1} = 9 v, U_{2} = 5.4 v, U_{3} = 3.6 v$ respectively.

Step by step solution

Given information

We need to find the charge on and the potential difference across each capacitor.

Simplify

The potential difference on the first capacitor is $∆ V_{1} = 9 V$ . And the charge will be

$q_{1} = C_{1} ∆ V = 5 \cdot 10^{- 6} \cdot 9 = 45 μ C$

As for the two other capacitors, their common capacitance will be

$C_{23} = \frac{C_{2} C_{3}}{C_{2} + C_{3}} = \frac{24 \cdot 10^{- 12}}{10 \cdot 10^{- 6}} = 2.4 μ C$

From that, the charge on both capacitors will be

$q_{2} = q_{3} = C_{23} ∆ V_{3} \Rightarrow ∆ V_{3} = \frac{C_{2}}{C_{3}} ∆ V_{3}$

So, now

$U_{3} = \frac{2}{3} U_{2}$

and

$U_{2} + U_{3} = 9$

Therefore, the solution will be

$U_{2} = 5.4 V U_{3} = 3.6 V$

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What are the charge on and the potential difference across each capacitor in FIGURE $P 26.58$ ?

Short Answer

Step by step solution

Given information

Simplify

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What are the charge on and the potential difference across each capacitor in FIGURE P26.58?

Short Answer

Step by step solution

Given information

Simplify

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Measurements

Electromagnetism

Physical Quantities And Units

Famous Physicists

Engineering Physics

Study anywhere. Anytime. Across all devices.

What are the charge on and the potential difference across each capacitor in FIGURE $P 26.58$ ?