For the system of capacitors shown in Fig. E24.1624.16, find the equivalent capacitance between bb and cc.

Ch 24: Capacitance and Dielectrics

Young & Freedman Calc - University Physics 14th Edition

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Young & Freedman Calc 14th Edition

Ch 24: Capacitance and Dielectrics

Problem 16a

Chapter 24, Problem 16a

For the system of capacitors shown in Fig. E $24.16$ , find the equivalent capacitance between $b$ and $c$ .

Verified step by step guidance

Identify the capacitors between points b and c. There are two capacitors in parallel: one with a capacitance of 9.0 pF and the other with a capacitance of 11 pF.

Recall that for capacitors in parallel, the equivalent capacitance (C_eq) is the sum of the individual capacitances. Use the formula: C_eq = C_1 + C_2.

Substitute the given values into the formula: C_eq = 9.0 pF + 11 pF.

Calculate the sum to find the equivalent capacitance between points b and c.

The result from the calculation will give you the equivalent capacitance between points b and c in picofarads (pF).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Capacitance

Capacitance is the ability of a capacitor to store electrical energy in an electric field, measured in farads (F). It is defined as the charge stored per unit voltage across the capacitor. In this problem, capacitors are given in picofarads (pF), which is a common unit for small capacitances.

Series and Parallel Capacitors

Capacitors can be connected in series or parallel, affecting the total capacitance of the circuit. In series, the total capacitance (C_total) is given by the reciprocal of the sum of the reciprocals of individual capacitances: 1/C_total = 1/C1 + 1/C2. In parallel, the total capacitance is the sum of the individual capacitances: C_total = C1 + C2. This question involves both configurations.

Equivalent Capacitance

The equivalent capacitance is the total capacitance of a combination of capacitors that can be treated as a single capacitor. To find the equivalent capacitance between points b and c in the given circuit, one must first calculate the capacitance of the parallel combination of the 9 pF and 11 pF capacitors, and then combine that result with the 15 pF capacitor in series.

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Find Equivalent Capacitance #1

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Textbook Question

Figure E $24.14$ shows a system of four capacitors, where the potential difference across ab is $50.0$ V. How much charge is stored in each of the $10.0$ - $μ$ F and the $9.0$ - $μ$ F capacitors?

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Textbook Question

In Fig. E $24.20$ , $C sub 1 equals 6.00$ $μ$ F, $C sub 2 equals 3.00$ $μ$ F, and $C sub 3 equals 5.00$ $μ$ F. The capacitor network is connected to an applied potential $V_{a b}$ .

(a) After the charges on the capacitors have reached their final values, the charge on $C sub 2$ is $30.0$ mC. What are the charges on capacitors $C sub 1$ and $C sub 3$ ?

(b) What is the applied voltage $V_{a b}$ ?

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Textbook Question

A $5.80$ - $μ$ F, parallel-plate, air capacitor has a plate separation of $5.00$ mm and is charged to a potential difference of $400$ V. Calculate the energy density in the region between the plates, in units of J/m³.

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Textbook Question

Figure E $24.14$ shows a system of four capacitors, where the potential difference across ab is $50.0$ V. How much charge is stored by this combination of capacitors?

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Textbook Question

A parallel-plate air capacitor has a capacitance of 920 pF. The charge on each plate is 3.90 uC. (a) What is the potential difference between the plates? (b) If the charge is kept constant, what will be the potential difference if the plate separation is doubled? (c) How much work is required to double the separation?

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Textbook Question

A spherical capacitor contains a charge of $3.30$ nC when connected to a potential difference of $220$ V. If its plates are separated by vacuum and the inner radius of the outer shell is $4.00$ cm, calculate: (a) the capacitance; (b) the radius of the inner sphere; (c) the electric field just outside the surface of the inner sphere.

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