Chapter 26: Q. 56 (page 740)

What are the charge on and the potential difference across each capacitor in FIGURE $P 26.56$ ?

Short Answer

Expert verified

The charge on each capacitor is $60 μ C$ , and the potential difference is respectively $V_{1} = 5 V, V_{2} = 15 V, V_{3} = 10 V$ .

Step by step solution

Given information

We have given that the FIGURE $P 26.56$ .

We need to find the charge on and the potential difference across each capacitor in FIGURE $P 26.56$ .

Simplify

If the capacitors are connected in series the charge on every capacitor is the same, and it is equal to the charge of a single equivalent capacitor. The expression for the equivalent capacitance $C$ of this series is given by

$\frac{1}{C} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}}$ .

This yields

$\frac{1}{C} = \frac{C_{2} C_{3}}{C_{1} C_{2} C_{3}} + \frac{C_{1} C_{3}}{C_{1} C_{2} C_{3}} + \frac{C_{1} C_{2}}{C_{1} C_{2} C_{3}}$ ,

$C = \frac{C_{1} C_{2} C_{3}}{C_{1} C_{2} + C_{2} C_{3} + C_{1} C_{3}} = 2 μ F$ .

Therefore the charge on each capacitor is

$q = C V = 60 μ C$ .

Then the potential difference on each capacitor is given as

$V_{1} = \frac{q}{C_{1}} = 5 V, V_{2} = \frac{q}{C_{2}} = 15 V, V_{3} = \frac{q}{C_{3}} = 10 V .$

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What are the charge on and the potential difference across each capacitor in FIGURE $P 26.56$ ?

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 P26.56?

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

Fundamentals of Physics

Dynamics

Circular Motion and Gravitation

Classical Mechanics

Further Mechanics and Thermal Physics

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

What are the charge on and the potential difference across each capacitor in FIGURE $P 26.56$ ?