Figure E24.1424.1424.14 shows a system of four capacitors, where the potential difference across ab is 50.050.050.0 V. How much charge is stored in each of the 10.010.0-μ\muF and the 9.09.0-μ\muF capacitors?

Ch 24: Capacitance and Dielectrics

Young & Freedman Calc - University Physics 14th Edition

Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook

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Young & Freedman Calc 14th Edition

Ch 24: Capacitance and Dielectrics

Problem 14c

Chapter 24, Problem 14c

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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Identify the configuration of the capacitors in the circuit. The 10.0 μF and 9.0 μF capacitors are in series with the 5.0 μF and 8.0 μF capacitors, which are in parallel.

Calculate the equivalent capacitance of the parallel capacitors (5.0 μF and 8.0 μF). Use the formula for capacitors in parallel: C_parallel = C2 + C3, where C2 = 5.0 μF and C3 = 8.0 μF.

Determine the equivalent capacitance of the series capacitors (10.0 μF and 9.0 μF) with the equivalent parallel capacitance. Use the formula for capacitors in series: 1/C_series = 1/C1 + 1/C_parallel + 1/C4, where C1 = 10.0 μF and C4 = 9.0 μF.

Calculate the charge stored in the 10.0 μF capacitor using the formula Q = C * V, where C is the capacitance and V is the potential difference across the capacitor. The potential difference across the series capacitors is the same as the total potential difference (50.0 V).

Calculate the charge stored in the 9.0 μF capacitor using the same formula Q = C * V, considering the potential difference across the series capacitors.

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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 charge per unit voltage, defined as C = Q/V, where C is capacitance in farads, Q is charge in coulombs, and V is voltage in volts. In this problem, the capacitors have values in microfarads (µF), which is a common unit for small capacitances. Understanding capacitance is essential for calculating the charge stored in each capacitor when a potential difference is applied.

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 1/C_total = 1/C1 + 1/C2 + ... for each capacitor. In parallel, the total capacitance is the sum of individual capacitances: C_total = C1 + C2 + ... Understanding how to combine capacitors in these configurations is crucial for solving the problem regarding the charge distribution across the capacitors.

Charge Distribution

When capacitors are connected in a circuit with a voltage applied, the charge stored on each capacitor depends on its capacitance and the voltage across it. For capacitors in parallel, they share the same voltage, while in series, the charge is the same across each capacitor. This concept is vital for determining how much charge is stored in the 10.0 µF and 9.0 µF capacitors when a 50.0 V potential difference is applied across the entire system.

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Textbook Question

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

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

A capacitor is made from two hollow, coaxial, iron cylinders, one inside the other. The inner cylinder is negatively charged and the outer is positively charged; the magnitude of the charge on each is $10.0$ pC. The inner cylinder has radius $0.50$ mm, the outer one has radius $5.00$ mm, and the length of each cylinder is $18.0$ cm.

(a) What is the capacitance?

(b) What applied potential difference is necessary to produce these charges on the cylinders?

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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 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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Figure E24.1424.1424.14 shows a system of four capacitors, where the potential difference across ab is 50.050.050.0 V. How much charge is stored in each of the 10.010.0-μ\(\mu\)F and the 9.09.0-μ\(\mu\)F capacitors?

Verified video answer for a similar problem:

Key Concepts

Capacitance

Series and Parallel Capacitors

Charge Distribution

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?