Ch 26: Potential and Field

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 26: Potential and Field

Problem 83

Chapter 26, Problem 83

Each capacitor in FIGURE CP26.83 has capacitance C. What is the equivalent capacitance between points a and b?

Verified step by step guidance

Step 1: Analyze the circuit diagram. The capacitors are arranged in a combination of series and parallel configurations. Identify the groups of capacitors that are in series and those that are in parallel.

Step 2: For capacitors in series, use the formula for equivalent capacitance:

C_{eq} = \frac{1}{1 / C_{1} + 1 / C_{2}}

. Apply this formula to the capacitors that are connected in series.

Step 3: For capacitors in parallel, use the formula for equivalent capacitance:

C_{eq} = C_{1} + C_{2}

. Apply this formula to the capacitors that are connected in parallel.

Step 4: Combine the results from steps 2 and 3 iteratively, simplifying the circuit step by step until you find the total equivalent capacitance between points a and b.

Step 5: Ensure that the final equivalent capacitance is expressed in terms of the given capacitance C, as all capacitors in the circuit have the same capacitance value.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

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 charge per unit voltage. It is measured in farads (F) and is defined as the ratio of the charge (Q) stored on one plate to the voltage (V) across the plates, expressed as C = Q/V. Understanding capacitance is crucial for analyzing how capacitors behave in circuits.

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, resulting in a lower total capacitance. In parallel, the total capacitance is the sum of individual capacitances: C_total = C1 + C2 + .... This distinction is essential for calculating the equivalent capacitance between points a and b.

Equivalent Capacitance

The equivalent capacitance is a single capacitance value that can replace a network of capacitors while maintaining the same electrical behavior. It simplifies circuit analysis by allowing the calculation of total charge and voltage across the network. To find the equivalent capacitance between points a and b, one must apply the rules for series and parallel combinations based on the configuration of the capacitors in the circuit.

Recommended video:

Guided course

03:44

Find Equivalent Capacitance #1

Related Practice

Textbook Question

Consider a uniformly charged sphere of radius R and total charge Q. The electric field E_out outside the sphere (r≥R) is simply that of a point charge Q. In Chapter 24, we used Gauss’s law to find that the electric field E_in inside the sphere (r≤R) is radially outward with field strength $E i n = \frac{1}{4 π ϵ_{0}} \frac{Q}{R^{3}} r$ . What is the ratio V_center/V_surface?

1930

views

Textbook Question

Find an expression for the capacitance of a spherical capacitor, consisting of concentric spherical shells of radii R₁ (inner shell) and R₂ (outer shell).

141

views

Textbook Question

A spherical capacitor with a 1.0 mm gap between the shells has a capacitance of 100 pF. What are the diameters of the two spheres?

views