PHYSICS 1250 PACKAGE >CI<
PHYSICS 1250 PACKAGE >CI<
9th Edition
ISBN: 9781305000988
Author: SERWAY
Publisher: CENGAGE LEARNING (CUSTOM)
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Chapter 26, Problem 26.23P

Four capacitors are connected as shown in Figure P25.11. (a) Find the equivalent capacitance between points a and b. (b) Calculate the charge on each capacitor, taking ΔVab = 15.0 V.

Figure P25.11

Chapter 26, Problem 26.23P, Four capacitors are connected as shown in Figure P25.11. (a) Find the equivalent capacitance between

(a)

Expert Solution
Check Mark
To determine
The equivalent capacitance between a and b .

Answer to Problem 26.23P

The equivalent capacitance between a and b is 5.96μF .

Explanation of Solution

Given information:

The four capacitors are connected in figure given below:

PHYSICS 1250 PACKAGE >CI<, Chapter 26, Problem 26.23P , additional homework tip  1

Figure (1)

Explanation:

The capacitors 15.0μFand3.00μF are in series.

Formula to calculate the equivalent capacitance when they are connected in series.

CS=C15.0μF×C3.00μFC15.0μF+C3.00μF (1)

Here,

CS is the equivalent capacitance when they are connected in series.

Substitute 15.0μF for C15.0μF , 3.00μF for C3.00μF in equation (1) to find CS ,

CS=15.0μF×3.00μF15.0μF+3.00μF=2.50μF

The capacitors CS and 6.00μF are in parallel.

Formula to calculate the equivalent capacitance when they are connected in parallel.

CP=CS+C6.00μF (2)

Here,

CP is the equivalent capacitance when they are connected in parallel.

Substitute 2.50μF for CS , 6.00μF for C6.00μF in equation (1) to find CP ,

CP=2.50μF+6.00μF=8.50μF

The capacitors CP and 20.0μF are in series.

Formula to calculate the equivalent capacitance when they are connected in series.

Ceq=CP×C20.0μFCP+C20.0μF (3)

Here,

Ceq is the equivalent capacitance between a and b.

Substitute 8.50μF for CP , 20.0μF for C20.0μF in equation (1) to find Ceq ,

Ceq=8.50μF×20.0μF8.50μF+20.0μF=5.96μF

Thus, the equivalent capacitance between a and b is 5.96μF .

Conclusion:

Therefore, the equivalent capacitance between a and b is 5.96μF .

(b)

Expert Solution
Check Mark
To determine
The charge on each capacitor.

Answer to Problem 26.23P

The charge across capacitors 15.0μFand3.00μF is C2 is 26.3μC , the charge through 20.0μF is 89.5μC , the charge across 6.00μF capacitor is 63.2μC .

Explanation of Solution

Given information:

The voltage across a and b is 15.0V , the four capacitors are connected in figure given below:

PHYSICS 1250 PACKAGE >CI<, Chapter 26, Problem 26.23P , additional homework tip  2

Explanation:

Formula to calculate the total charge in the circuit.

Qtotal=Ceq×ΔVab (4)

Here,

Qtotal is the total charge in the circuit.

ΔVab is the voltage across a and b.

Substitute 15.0V for ΔVab , 5.965μF for Ceq , in equation (3) to find VCP ,

Qtotal=5.965μF×15.0V=89.475μCQ20.0μF89.5μC

Thus, the total charge in the circuit and the charge through 20.0μF is 89.5μC .

Formula to calculate the potential drop across 20.0μF capacitor.

ΔV20.0μF=Q20.0μFC20.0μF (5)

Substitute 20.0μF for C20.0μF , 89.5μC for Q20.0μF , in equation (5) to find ΔV20.0μF ,

ΔV20.0μF=89.5μC20.0μF=4.475V

Thus, the potential drop across 20.0μF capacitor is 4.475V .

Formula to calculate the potential drop across 6.00μF capacitor.

ΔV6.00μF=ΔVabΔV20.0μF (6)

Substitute 15.0V for ΔVab , 4.475V for ΔV20.0μF , in equation (6) to find ΔV6.00μF ,

ΔV6.00μF=15.0V4.475V=10.525V

Thus, the potential drop across 6.00μF capacitor is 10.525V .

Formula to calculate the charge across 6.00μF capacitor.

Q6.00μF=C6.00μF×ΔV6.00μF (7)

Substitute 6.00μF for C6.00μF , 10.525V for ΔV6.00μF in equation (7) to find Q6.00μF ,

Q6.00μF=6.00μF×10.525V=63.15μC63.2μC

Thus, the charge across 6.00μF capacitor is 63.2μC .

The charge across capacitors 15.0μFand3.00μF will be same.

Calculate the charge for the capacitor 15.0μFand3.00μF .

Q15.0μF=Q3.00μF=Q20.0μFQ6.00μF (8)

Substitute 89.5μC for Q20.0μF , 63.2μC for Q6.00μF in equation (8) to find Q15.0μFandQ3.00μF ,

Q15.0μFand3.00μF=89.5μC63.2μC=26.3μC

Thus, the charge across capacitors 15.0μFand3.00μF is C2 is 26.3μC .

Conclusion:

Therefore, the charge across capacitors 15.0μFand3.00μF is C2 is 26.3μC , the charge through 20.0μF is 89.5μC , the charge across 6.00μF capacitor is 63.2μC .

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Chapter 26 Solutions

PHYSICS 1250 PACKAGE >CI<

Ch. 26 - Assume a device is designed to obtain a large...Ch. 26 - (i) What happens to the magnitude of the charge...Ch. 26 - A capacitor with very large capacitance is in...Ch. 26 - A parallel-plate capacitor filled with air carries...Ch. 26 - (i) A battery is attached to several different...Ch. 26 - A parallel-plate capacitor is charged and then is...Ch. 26 - (i) Rank the following five capacitors from...Ch. 26 - True or False? (a) From the definition of...Ch. 26 - You charge a parallel-plate capacitor, remove it...Ch. 26 - (a) Why is it dangerous to touch the terminals of...Ch. 26 - Assume you want to increase the maximum operating...Ch. 26 - If you were asked to design a capacitor in which...Ch. 26 - Prob. 26.4CQCh. 26 - Explain why the work needed to move a particle...Ch. 26 - An air-filled capacitor is charged, then...Ch. 26 - The sum of the charges on both plates of a...Ch. 26 - Because the charges on the plates of a...Ch. 26 - (a) When a battery is connected to the plates of a...Ch. 26 - Two conductors having net charges of +10.0 C and...Ch. 26 - (a) How much charge is on each plate of a 4.00-F...Ch. 26 - An air-filled parallel-plate capacitor has plates...Ch. 26 - A 50.0-in length of coaxial cable has an inner...Ch. 26 - (a) Regarding (lie Earth and a cloud layer 800 m...Ch. 26 - When a potential difference of 150 V is applied to...Ch. 26 - Prob. 26.8PCh. 26 - An air-filled capacitor consists of two parallel...Ch. 26 - A variable air capacitor used in a radio tuning...Ch. 26 - An isolated, charged conducting sphere of radius...Ch. 26 - Review. A small object of mass m carries a charge...Ch. 26 - Two capacitors, C1 = 5.00 F and C2 = 12.0 F, are...Ch. 26 - What If? The two capacitors of Problem 13 (C1 =...Ch. 26 - Find the equivalent capacitance of a 4.20-F...Ch. 26 - Prob. 26.16PCh. 26 - According to its design specification, the timer...Ch. 26 - Why is the following situation impossible? A...Ch. 26 - For the system of four capacitors shown in Figure...Ch. 26 - Three capacitors are connected to a battery as...Ch. 26 - A group of identical capacitors is connected first...Ch. 26 - (a) Find the equivalent capacitance between points...Ch. 26 - Four capacitors are connected as shown in Figure...Ch. 26 - Consider the circuit shown in Figure P26.24, where...Ch. 26 - Find the equivalent capacitance between points a...Ch. 26 - Find (a) the equivalent capacitance of the...Ch. 26 - Two capacitors give an equivalent capacitance of...Ch. 26 - Two capacitors give an equivalent capacitance of...Ch. 26 - Consider three capacitors C1, C2. and C3 and a...Ch. 26 - The immediate cause of many deaths is ventricular...Ch. 26 - A 12.0-V battery is connected to a capacitor,...Ch. 26 - A 3.00-F capacitor is connected to a 12.0-V...Ch. 26 - As a person moves about in a dry environment,...Ch. 26 - Two capacitors, C1 = 18.0 F and C2 = 36.0 F, are...Ch. 26 - Two identical parallel-plate capacitors, each with...Ch. 26 - Two identical parallel-plate capacitors, each with...Ch. 26 - Two capacitors, C1 = 25.0 F and C2 = 5.00 F, are...Ch. 26 - A parallel-plate capacitor has a charge Q and...Ch. 26 - Review. A storm cloud and the ground represent the...Ch. 26 - Consider two conducting spheres with radii R1 and...Ch. 26 - Review. The circuit in Figure P26.41 (page 804)...Ch. 26 - A supermarket sells rolls of aluminum foil,...Ch. 26 - (a) How much charge can be placed 011 a capacitor...Ch. 26 - The voltage across an air-filled parallel-plate...Ch. 26 - Determine (a) the capacitance and (b) the maximum...Ch. 26 - A commercial capacitor is to be constructed as...Ch. 26 - A parallel-plate capacitor in air has a plate...Ch. 26 - Each capacitor in the combination shown in Figure...Ch. 26 - A 2.00-nF parallel-plate capacitor is charged to...Ch. 26 - A small rigid object carries positive and negative...Ch. 26 - An infinite line of positive charge lies along the...Ch. 26 - A small object with electric dipole moment p is...Ch. 26 - The general form of Gausss law describes how a...Ch. 26 - Find the equivalent capacitance of' the group of...Ch. 26 - Four parallel metal plates P1, P2, P3, and P4,...Ch. 26 - For (he system of four capacitors shown in Figure...Ch. 26 - A uniform electric field E = 3 000 V/m exists...Ch. 26 - Two large, parallel metal plates, each of area A,...Ch. 26 - A parallel-plate capacitor is constructed using a...Ch. 26 - Why is the following situation impossible? A...Ch. 26 - Prob. 26.61APCh. 26 - A parallel-plate capacitor with vacuum between its...Ch. 26 - A 10.0-F capacitor is charged to 15.0 V. It is...Ch. 26 - Assume that the internal diameter of the...Ch. 26 - Two square plates of sides are placed parallel to...Ch. 26 - (a) Two spheres have radii a and b, and their...Ch. 26 - A capacitor of unknown capacitance has been...Ch. 26 - A parallel-plate capacitor of plate separation d...Ch. 26 - Prob. 26.69APCh. 26 - Example 25.1 explored a cylindrical capacitor of...Ch. 26 - To repair a power supply for a stereo amplifier,...Ch. 26 - The inner conductor of a coaxial cable has a...Ch. 26 - Some physical systems possessing capacitance...Ch. 26 - Consider two long, parallel, and oppositely...Ch. 26 - Determine the equivalent capacitance of the...Ch. 26 - A parallel-plate capacitor with plates of area LW...Ch. 26 - Calculate the equivalent capacitance between...Ch. 26 - A capacitor is constructed from two square,...
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