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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

01

Given information

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

02

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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Most popular questions from this chapter

What is the equivalent capacitance of the three capacitors in Figure $E x 26.28$ ?

The two metal spheres in Figure Q26.9 are connected by a metal wire with a switch in the middle. Initially the switch is open. Sphere 1, with the larger radius, is given a positive charge. Sphere 2, with the smaller radius, is neutral. Then the switch is closed. Afterward, sphere 1 has charge $Q_{1}$ , is at potential $V_{1}$ , and the electric field strength at its surface is $E_{1}$ . The values for sphere 2 are $Q_{2}, V_{2}, and E_{2}$ .

a. Is $V_{1}$ larger than, smaller than, or equal to $V_{2}$ ? Explain.

b. Is $Q_{1}$ larger than, smaller than, or equal to $Q_{2}$ ? Explain.

c. Is $E_{1}$ larger than, smaller than, or equal to $E_{2}$ ? Explain.

You need to construct a 100 pF capacitor for a science project. You plan to cut two L * L metal squares and insert small spacers between their corners. The thinnest spacers you have are 0.20 mm thick. What is the proper value of L?

Two $4.0 c m \times 4.0 c m$ metal plates are separated by a $0.20 m m$ -thick piece of Teflon.

a. What is the capacitance?

b. What is the maximum potential difference between the plates?

Two $2.0 c m \times 2.0 c m$ metal electrodes are spaced $1.0 m m$ apart and connected by wires to the terminals of a $9.0 V$ battery.

a. What are the charge on each electrode and the potential difference between them? While the plates are still connected to the battery, insulated handles are used to pull them apart to a new spacing of $2.0 m m$ .

b. What are the charge on each electrode and the potential difference between them?

See all solutions

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