EXAMPLE 16.8 GOAL Find an equivalent capacitance of capacitors in series, and the charge and voltage...
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EXAMPLE 16.8 GOAL Find an equivalent capacitance of capacitors in series, and the charge and voltage on each capacitor. Four Capacitors Connected in Series PROBLEM Four capacitors are connected in series with a battery, as in the figure (a) Calculate the capacitance of the equivalent capacitor. (b) Compute the charge on the 12-μF capacitor. (c) Find the voltage drop across the 12-μF capacitor. SOLUTION (A) Calculate the equivalent capacitance of the series. Apply the series combination equivalent capacitance equation. 1 Ceq Four capacitors connected in series. STRATEGY Combine all the capacitors into a single, equivalent capacitor. Find the charge on this equivalent capacitor using C= Q/AV. This charge is the same as on the individual capacitors. Use this same equation again to find the voltage drop across the 12-µF capacitor. Ceq (B) Compute the charge on the 12-μF capacitor. The desired charge equals the charge on the equivalent capacitor: (C) Find the voltage drop across the 12-μF capacitor. Apply the basic capacitance equation. 5.0μF 6.0μF 12µF H c=2 1 1 1 1 + 3.0 UF 6.0 μF 12 μF 24 UF 1.6 μF QCqAV (1.6 x 106 F) (18 V) 29 μC → AV- Av. 18 V Ο 29 με 12 UF 24 μF = 2.4 V LEARN MORE REMARKS Notice that the equivalent capacitance is less than that of any of the individual capacitors. The relationship C Q/AV can be used to find the voltage drops on the other capacitors, just as in part (c). QUESTION Over which capacitor is the voltage drop the smallest? 81322.2 QUESTION Over which capacitor is the voltage drop the smallest? the 3.0-μF capacitor the 6.0-μF capacitor the 12-μF capacitor the 24-µF capacitor Over which capacitor is the voltage drop the largest? the 3.0-µF capacitor the 6.0-μF capacitor the 12-µF capacitor O the 24-µF capacitor PRACTICE IT Use the worked example above to help you solve this problem. Four capacitors are connected in series with a battery, as in the figure below, where C₁ = 3.52 μF, C₂ = 6.57 UF, C3= 13.0 μF, C4 = 24.7 μF, V 18.8 V. Ci HH C₂ C₂ Ca (a) Calculate the capacitance of the equivalent capacitor. 1.45 (b) Compute the charge on C3- μC X Your response differs from the correct answer by more than 10%. Double check your calculations. UF = = (a) Calculate the capacitance of the equivalent capacitor. 1.45 X (b) Compute the charge on C3. μc = Your response differs from the correct answer by more than 10%. Double check your calculations. UF (c) Find the voltage drop across C3. V EXERCISE HINTS: GETTING STARTED I I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. C4 is removed from the circuit, leaving only three capacitors in series. (a) Find the equivalent capacitance. Ceq = UF = (b) Find the charge on C₂. Q = μC (c) Find the voltage drop across C₂- AV = V EXAMPLE 16.8 GOAL Find an equivalent capacitance of capacitors in series, and the charge and voltage on each capacitor. Four Capacitors Connected in Series PROBLEM Four capacitors are connected in series with a battery, as in the figure (a) Calculate the capacitance of the equivalent capacitor. (b) Compute the charge on the 12-μF capacitor. (c) Find the voltage drop across the 12-μF capacitor. SOLUTION (A) Calculate the equivalent capacitance of the series. Apply the series combination equivalent capacitance equation. 1 Ceq Four capacitors connected in series. STRATEGY Combine all the capacitors into a single, equivalent capacitor. Find the charge on this equivalent capacitor using C= Q/AV. This charge is the same as on the individual capacitors. Use this same equation again to find the voltage drop across the 12-µF capacitor. Ceq (B) Compute the charge on the 12-μF capacitor. The desired charge equals the charge on the equivalent capacitor: (C) Find the voltage drop across the 12-μF capacitor. Apply the basic capacitance equation. 5.0μF 6.0μF 12µF H c=2 1 1 1 1 + 3.0 UF 6.0 μF 12 μF 24 UF 1.6 μF QCqAV (1.6 x 106 F) (18 V) 29 μC → AV- Av. 18 V Ο 29 με 12 UF 24 μF = 2.4 V LEARN MORE REMARKS Notice that the equivalent capacitance is less than that of any of the individual capacitors. The relationship C Q/AV can be used to find the voltage drops on the other capacitors, just as in part (c). QUESTION Over which capacitor is the voltage drop the smallest? 81322.2 QUESTION Over which capacitor is the voltage drop the smallest? the 3.0-μF capacitor the 6.0-μF capacitor the 12-μF capacitor the 24-µF capacitor Over which capacitor is the voltage drop the largest? the 3.0-µF capacitor the 6.0-μF capacitor the 12-µF capacitor O the 24-µF capacitor PRACTICE IT Use the worked example above to help you solve this problem. Four capacitors are connected in series with a battery, as in the figure below, where C₁ = 3.52 μF, C₂ = 6.57 UF, C3= 13.0 μF, C4 = 24.7 μF, V 18.8 V. Ci HH C₂ C₂ Ca (a) Calculate the capacitance of the equivalent capacitor. 1.45 (b) Compute the charge on C3- μC X Your response differs from the correct answer by more than 10%. Double check your calculations. UF = = (a) Calculate the capacitance of the equivalent capacitor. 1.45 X (b) Compute the charge on C3. μc = Your response differs from the correct answer by more than 10%. Double check your calculations. UF (c) Find the voltage drop across C3. V EXERCISE HINTS: GETTING STARTED I I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. C4 is removed from the circuit, leaving only three capacitors in series. (a) Find the equivalent capacitance. Ceq = UF = (b) Find the charge on C₂. Q = μC (c) Find the voltage drop across C₂- AV = V EXAMPLE 16.8 GOAL Find an equivalent capacitance of capacitors in series, and the charge and voltage on each capacitor. Four Capacitors Connected in Series PROBLEM Four capacitors are connected in series with a battery, as in the figure (a) Calculate the capacitance of the equivalent capacitor. (b) Compute the charge on the 12-μF capacitor. (c) Find the voltage drop across the 12-μF capacitor. SOLUTION (A) Calculate the equivalent capacitance of the series. Apply the series combination equivalent capacitance equation. 1 Ceq Four capacitors connected in series. STRATEGY Combine all the capacitors into a single, equivalent capacitor. Find the charge on this equivalent capacitor using C= Q/AV. This charge is the same as on the individual capacitors. Use this same equation again to find the voltage drop across the 12-µF capacitor. Ceq (B) Compute the charge on the 12-μF capacitor. The desired charge equals the charge on the equivalent capacitor: (C) Find the voltage drop across the 12-μF capacitor. Apply the basic capacitance equation. 5.0μF 6.0μF 12µF H c=2 1 1 1 1 + 3.0 UF 6.0 μF 12 μF 24 UF 1.6 μF QCqAV (1.6 x 106 F) (18 V) 29 μC → AV- Av. 18 V Ο 29 με 12 UF 24 μF = 2.4 V LEARN MORE REMARKS Notice that the equivalent capacitance is less than that of any of the individual capacitors. The relationship C Q/AV can be used to find the voltage drops on the other capacitors, just as in part (c). QUESTION Over which capacitor is the voltage drop the smallest? 81322.2 QUESTION Over which capacitor is the voltage drop the smallest? the 3.0-μF capacitor the 6.0-μF capacitor the 12-μF capacitor the 24-µF capacitor Over which capacitor is the voltage drop the largest? the 3.0-µF capacitor the 6.0-μF capacitor the 12-µF capacitor O the 24-µF capacitor PRACTICE IT Use the worked example above to help you solve this problem. Four capacitors are connected in series with a battery, as in the figure below, where C₁ = 3.52 μF, C₂ = 6.57 UF, C3= 13.0 μF, C4 = 24.7 μF, V 18.8 V. Ci HH C₂ C₂ Ca (a) Calculate the capacitance of the equivalent capacitor. 1.45 (b) Compute the charge on C3- μC X Your response differs from the correct answer by more than 10%. Double check your calculations. UF = = (a) Calculate the capacitance of the equivalent capacitor. 1.45 X (b) Compute the charge on C3. μc = Your response differs from the correct answer by more than 10%. Double check your calculations. UF (c) Find the voltage drop across C3. V EXERCISE HINTS: GETTING STARTED I I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. C4 is removed from the circuit, leaving only three capacitors in series. (a) Find the equivalent capacitance. Ceq = UF = (b) Find the charge on C₂. Q = μC (c) Find the voltage drop across C₂- AV = V EXAMPLE 16.8 GOAL Find an equivalent capacitance of capacitors in series, and the charge and voltage on each capacitor. Four Capacitors Connected in Series PROBLEM Four capacitors are connected in series with a battery, as in the figure (a) Calculate the capacitance of the equivalent capacitor. (b) Compute the charge on the 12-μF capacitor. (c) Find the voltage drop across the 12-μF capacitor. SOLUTION (A) Calculate the equivalent capacitance of the series. Apply the series combination equivalent capacitance equation. 1 Ceq Four capacitors connected in series. STRATEGY Combine all the capacitors into a single, equivalent capacitor. Find the charge on this equivalent capacitor using C= Q/AV. This charge is the same as on the individual capacitors. Use this same equation again to find the voltage drop across the 12-µF capacitor. Ceq (B) Compute the charge on the 12-μF capacitor. The desired charge equals the charge on the equivalent capacitor: (C) Find the voltage drop across the 12-μF capacitor. Apply the basic capacitance equation. 5.0μF 6.0μF 12µF H c=2 1 1 1 1 + 3.0 UF 6.0 μF 12 μF 24 UF 1.6 μF QCqAV (1.6 x 106 F) (18 V) 29 μC → AV- Av. 18 V Ο 29 με 12 UF 24 μF = 2.4 V LEARN MORE REMARKS Notice that the equivalent capacitance is less than that of any of the individual capacitors. The relationship C Q/AV can be used to find the voltage drops on the other capacitors, just as in part (c). QUESTION Over which capacitor is the voltage drop the smallest? 81322.2 QUESTION Over which capacitor is the voltage drop the smallest? the 3.0-μF capacitor the 6.0-μF capacitor the 12-μF capacitor the 24-µF capacitor Over which capacitor is the voltage drop the largest? the 3.0-µF capacitor the 6.0-μF capacitor the 12-µF capacitor O the 24-µF capacitor PRACTICE IT Use the worked example above to help you solve this problem. Four capacitors are connected in series with a battery, as in the figure below, where C₁ = 3.52 μF, C₂ = 6.57 UF, C3= 13.0 μF, C4 = 24.7 μF, V 18.8 V. Ci HH C₂ C₂ Ca (a) Calculate the capacitance of the equivalent capacitor. 1.45 (b) Compute the charge on C3- μC X Your response differs from the correct answer by more than 10%. Double check your calculations. UF = = (a) Calculate the capacitance of the equivalent capacitor. 1.45 X (b) Compute the charge on C3. μc = Your response differs from the correct answer by more than 10%. Double check your calculations. UF (c) Find the voltage drop across C3. V EXERCISE HINTS: GETTING STARTED I I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. C4 is removed from the circuit, leaving only three capacitors in series. (a) Find the equivalent capacitance. Ceq = UF = (b) Find the charge on C₂. Q = μC (c) Find the voltage drop across C₂- AV = V EXAMPLE 16.8 GOAL Find an equivalent capacitance of capacitors in series, and the charge and voltage on each capacitor. Four Capacitors Connected in Series PROBLEM Four capacitors are connected in series with a battery, as in the figure (a) Calculate the capacitance of the equivalent capacitor. (b) Compute the charge on the 12-μF capacitor. (c) Find the voltage drop across the 12-μF capacitor. SOLUTION (A) Calculate the equivalent capacitance of the series. Apply the series combination equivalent capacitance equation. 1 Ceq Four capacitors connected in series. STRATEGY Combine all the capacitors into a single, equivalent capacitor. Find the charge on this equivalent capacitor using C= Q/AV. This charge is the same as on the individual capacitors. Use this same equation again to find the voltage drop across the 12-µF capacitor. Ceq (B) Compute the charge on the 12-μF capacitor. The desired charge equals the charge on the equivalent capacitor: (C) Find the voltage drop across the 12-μF capacitor. Apply the basic capacitance equation. 5.0μF 6.0μF 12µF H c=2 1 1 1 1 + 3.0 UF 6.0 μF 12 μF 24 UF 1.6 μF QCqAV (1.6 x 106 F) (18 V) 29 μC → AV- Av. 18 V Ο 29 με 12 UF 24 μF = 2.4 V LEARN MORE REMARKS Notice that the equivalent capacitance is less than that of any of the individual capacitors. The relationship C Q/AV can be used to find the voltage drops on the other capacitors, just as in part (c). QUESTION Over which capacitor is the voltage drop the smallest? 81322.2 QUESTION Over which capacitor is the voltage drop the smallest? the 3.0-μF capacitor the 6.0-μF capacitor the 12-μF capacitor the 24-µF capacitor Over which capacitor is the voltage drop the largest? the 3.0-µF capacitor the 6.0-μF capacitor the 12-µF capacitor O the 24-µF capacitor PRACTICE IT Use the worked example above to help you solve this problem. Four capacitors are connected in series with a battery, as in the figure below, where C₁ = 3.52 μF, C₂ = 6.57 UF, C3= 13.0 μF, C4 = 24.7 μF, V 18.8 V. Ci HH C₂ C₂ Ca (a) Calculate the capacitance of the equivalent capacitor. 1.45 (b) Compute the charge on C3- μC X Your response differs from the correct answer by more than 10%. Double check your calculations. UF = = (a) Calculate the capacitance of the equivalent capacitor. 1.45 X (b) Compute the charge on C3. μc = Your response differs from the correct answer by more than 10%. Double check your calculations. UF (c) Find the voltage drop across C3. V EXERCISE HINTS: GETTING STARTED I I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. C4 is removed from the circuit, leaving only three capacitors in series. (a) Find the equivalent capacitance. Ceq = UF = (b) Find the charge on C₂. Q = μC (c) Find the voltage drop across C₂- AV = V EXAMPLE 16.8 GOAL Find an equivalent capacitance of capacitors in series, and the charge and voltage on each capacitor. Four Capacitors Connected in Series PROBLEM Four capacitors are connected in series with a battery, as in the figure (a) Calculate the capacitance of the equivalent capacitor. (b) Compute the charge on the 12-μF capacitor. (c) Find the voltage drop across the 12-μF capacitor. SOLUTION (A) Calculate the equivalent capacitance of the series. Apply the series combination equivalent capacitance equation. 1 Ceq Four capacitors connected in series. STRATEGY Combine all the capacitors into a single, equivalent capacitor. Find the charge on this equivalent capacitor using C= Q/AV. This charge is the same as on the individual capacitors. Use this same equation again to find the voltage drop across the 12-µF capacitor. Ceq (B) Compute the charge on the 12-μF capacitor. The desired charge equals the charge on the equivalent capacitor: (C) Find the voltage drop across the 12-μF capacitor. Apply the basic capacitance equation. 5.0μF 6.0μF 12µF H c=2 1 1 1 1 + 3.0 UF 6.0 μF 12 μF 24 UF 1.6 μF QCqAV (1.6 x 106 F) (18 V) 29 μC → AV- Av. 18 V Ο 29 με 12 UF 24 μF = 2.4 V LEARN MORE REMARKS Notice that the equivalent capacitance is less than that of any of the individual capacitors. The relationship C Q/AV can be used to find the voltage drops on the other capacitors, just as in part (c). QUESTION Over which capacitor is the voltage drop the smallest? 81322.2 QUESTION Over which capacitor is the voltage drop the smallest? the 3.0-μF capacitor the 6.0-μF capacitor the 12-μF capacitor the 24-µF capacitor Over which capacitor is the voltage drop the largest? the 3.0-µF capacitor the 6.0-μF capacitor the 12-µF capacitor O the 24-µF capacitor PRACTICE IT Use the worked example above to help you solve this problem. Four capacitors are connected in series with a battery, as in the figure below, where C₁ = 3.52 μF, C₂ = 6.57 UF, C3= 13.0 μF, C4 = 24.7 μF, V 18.8 V. Ci HH C₂ C₂ Ca (a) Calculate the capacitance of the equivalent capacitor. 1.45 (b) Compute the charge on C3- μC X Your response differs from the correct answer by more than 10%. Double check your calculations. UF = = (a) Calculate the capacitance of the equivalent capacitor. 1.45 X (b) Compute the charge on C3. μc = Your response differs from the correct answer by more than 10%. Double check your calculations. UF (c) Find the voltage drop across C3. V EXERCISE HINTS: GETTING STARTED I I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. C4 is removed from the circuit, leaving only three capacitors in series. (a) Find the equivalent capacitance. Ceq = UF = (b) Find the charge on C₂. Q = μC (c) Find the voltage drop across C₂- AV = V EXAMPLE 16.8 GOAL Find an equivalent capacitance of capacitors in series, and the charge and voltage on each capacitor. Four Capacitors Connected in Series PROBLEM Four capacitors are connected in series with a battery, as in the figure (a) Calculate the capacitance of the equivalent capacitor. (b) Compute the charge on the 12-μF capacitor. (c) Find the voltage drop across the 12-μF capacitor. SOLUTION (A) Calculate the equivalent capacitance of the series. Apply the series combination equivalent capacitance equation. 1 Ceq Four capacitors connected in series. STRATEGY Combine all the capacitors into a single, equivalent capacitor. Find the charge on this equivalent capacitor using C= Q/AV. This charge is the same as on the individual capacitors. Use this same equation again to find the voltage drop across the 12-µF capacitor. Ceq (B) Compute the charge on the 12-μF capacitor. The desired charge equals the charge on the equivalent capacitor: (C) Find the voltage drop across the 12-μF capacitor. Apply the basic capacitance equation. 5.0μF 6.0μF 12µF H c=2 1 1 1 1 + 3.0 UF 6.0 μF 12 μF 24 UF 1.6 μF QCqAV (1.6 x 106 F) (18 V) 29 μC → AV- Av. 18 V Ο 29 με 12 UF 24 μF = 2.4 V LEARN MORE REMARKS Notice that the equivalent capacitance is less than that of any of the individual capacitors. The relationship C Q/AV can be used to find the voltage drops on the other capacitors, just as in part (c). QUESTION Over which capacitor is the voltage drop the smallest? 81322.2 QUESTION Over which capacitor is the voltage drop the smallest? the 3.0-μF capacitor the 6.0-μF capacitor the 12-μF capacitor the 24-µF capacitor Over which capacitor is the voltage drop the largest? the 3.0-µF capacitor the 6.0-μF capacitor the 12-µF capacitor O the 24-µF capacitor PRACTICE IT Use the worked example above to help you solve this problem. Four capacitors are connected in series with a battery, as in the figure below, where C₁ = 3.52 μF, C₂ = 6.57 UF, C3= 13.0 μF, C4 = 24.7 μF, V 18.8 V. Ci HH C₂ C₂ Ca (a) Calculate the capacitance of the equivalent capacitor. 1.45 (b) Compute the charge on C3- μC X Your response differs from the correct answer by more than 10%. Double check your calculations. UF = = (a) Calculate the capacitance of the equivalent capacitor. 1.45 X (b) Compute the charge on C3. μc = Your response differs from the correct answer by more than 10%. Double check your calculations. UF (c) Find the voltage drop across C3. V EXERCISE HINTS: GETTING STARTED I I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. C4 is removed from the circuit, leaving only three capacitors in series. (a) Find the equivalent capacitance. Ceq = UF = (b) Find the charge on C₂. Q = μC (c) Find the voltage drop across C₂- AV = V EXAMPLE 16.8 GOAL Find an equivalent capacitance of capacitors in series, and the charge and voltage on each capacitor. Four Capacitors Connected in Series PROBLEM Four capacitors are connected in series with a battery, as in the figure (a) Calculate the capacitance of the equivalent capacitor. (b) Compute the charge on the 12-μF capacitor. (c) Find the voltage drop across the 12-μF capacitor. SOLUTION (A) Calculate the equivalent capacitance of the series. Apply the series combination equivalent capacitance equation. 1 Ceq Four capacitors connected in series. STRATEGY Combine all the capacitors into a single, equivalent capacitor. Find the charge on this equivalent capacitor using C= Q/AV. This charge is the same as on the individual capacitors. Use this same equation again to find the voltage drop across the 12-µF capacitor. Ceq (B) Compute the charge on the 12-μF capacitor. The desired charge equals the charge on the equivalent capacitor: (C) Find the voltage drop across the 12-μF capacitor. Apply the basic capacitance equation. 5.0μF 6.0μF 12µF H c=2 1 1 1 1 + 3.0 UF 6.0 μF 12 μF 24 UF 1.6 μF QCqAV (1.6 x 106 F) (18 V) 29 μC → AV- Av. 18 V Ο 29 με 12 UF 24 μF = 2.4 V LEARN MORE REMARKS Notice that the equivalent capacitance is less than that of any of the individual capacitors. The relationship C Q/AV can be used to find the voltage drops on the other capacitors, just as in part (c). QUESTION Over which capacitor is the voltage drop the smallest? 81322.2 QUESTION Over which capacitor is the voltage drop the smallest? the 3.0-μF capacitor the 6.0-μF capacitor the 12-μF capacitor the 24-µF capacitor Over which capacitor is the voltage drop the largest? the 3.0-µF capacitor the 6.0-μF capacitor the 12-µF capacitor O the 24-µF capacitor PRACTICE IT Use the worked example above to help you solve this problem. Four capacitors are connected in series with a battery, as in the figure below, where C₁ = 3.52 μF, C₂ = 6.57 UF, C3= 13.0 μF, C4 = 24.7 μF, V 18.8 V. Ci HH C₂ C₂ Ca (a) Calculate the capacitance of the equivalent capacitor. 1.45 (b) Compute the charge on C3- μC X Your response differs from the correct answer by more than 10%. Double check your calculations. UF = = (a) Calculate the capacitance of the equivalent capacitor. 1.45 X (b) Compute the charge on C3. μc = Your response differs from the correct answer by more than 10%. Double check your calculations. UF (c) Find the voltage drop across C3. V EXERCISE HINTS: GETTING STARTED I I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. C4 is removed from the circuit, leaving only three capacitors in series. (a) Find the equivalent capacitance. Ceq = UF = (b) Find the charge on C₂. Q = μC (c) Find the voltage drop across C₂- AV = V EXAMPLE 16.8 GOAL Find an equivalent capacitance of capacitors in series, and the charge and voltage on each capacitor. Four Capacitors Connected in Series PROBLEM Four capacitors are connected in series with a battery, as in the figure (a) Calculate the capacitance of the equivalent capacitor. (b) Compute the charge on the 12-μF capacitor. (c) Find the voltage drop across the 12-μF capacitor. SOLUTION (A) Calculate the equivalent capacitance of the series. Apply the series combination equivalent capacitance equation. 1 Ceq Four capacitors connected in series. STRATEGY Combine all the capacitors into a single, equivalent capacitor. Find the charge on this equivalent capacitor using C= Q/AV. This charge is the same as on the individual capacitors. Use this same equation again to find the voltage drop across the 12-µF capacitor. Ceq (B) Compute the charge on the 12-μF capacitor. The desired charge equals the charge on the equivalent capacitor: (C) Find the voltage drop across the 12-μF capacitor. Apply the basic capacitance equation. 5.0μF 6.0μF 12µF H c=2 1 1 1 1 + 3.0 UF 6.0 μF 12 μF 24 UF 1.6 μF QCqAV (1.6 x 106 F) (18 V) 29 μC → AV- Av. 18 V Ο 29 με 12 UF 24 μF = 2.4 V LEARN MORE REMARKS Notice that the equivalent capacitance is less than that of any of the individual capacitors. The relationship C Q/AV can be used to find the voltage drops on the other capacitors, just as in part (c). QUESTION Over which capacitor is the voltage drop the smallest? 81322.2 QUESTION Over which capacitor is the voltage drop the smallest? the 3.0-μF capacitor the 6.0-μF capacitor the 12-μF capacitor the 24-µF capacitor Over which capacitor is the voltage drop the largest? the 3.0-µF capacitor the 6.0-μF capacitor the 12-µF capacitor O the 24-µF capacitor PRACTICE IT Use the worked example above to help you solve this problem. Four capacitors are connected in series with a battery, as in the figure below, where C₁ = 3.52 μF, C₂ = 6.57 UF, C3= 13.0 μF, C4 = 24.7 μF, V 18.8 V. Ci HH C₂ C₂ Ca (a) Calculate the capacitance of the equivalent capacitor. 1.45 (b) Compute the charge on C3- μC X Your response differs from the correct answer by more than 10%. Double check your calculations. UF = = (a) Calculate the capacitance of the equivalent capacitor. 1.45 X (b) Compute the charge on C3. μc = Your response differs from the correct answer by more than 10%. Double check your calculations. UF (c) Find the voltage drop across C3. V EXERCISE HINTS: GETTING STARTED I I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. C4 is removed from the circuit, leaving only three capacitors in series. (a) Find the equivalent capacitance. Ceq = UF = (b) Find the charge on C₂. Q = μC (c) Find the voltage drop across C₂- AV = V EXAMPLE 16.8 GOAL Find an equivalent capacitance of capacitors in series, and the charge and voltage on each capacitor. Four Capacitors Connected in Series PROBLEM Four capacitors are connected in series with a battery, as in the figure (a) Calculate the capacitance of the equivalent capacitor. (b) Compute the charge on the 12-μF capacitor. (c) Find the voltage drop across the 12-μF capacitor. SOLUTION (A) Calculate the equivalent capacitance of the series. Apply the series combination equivalent capacitance equation. 1 Ceq Four capacitors connected in series. STRATEGY Combine all the capacitors into a single, equivalent capacitor. Find the charge on this equivalent capacitor using C= Q/AV. This charge is the same as on the individual capacitors. Use this same equation again to find the voltage drop across the 12-µF capacitor. Ceq (B) Compute the charge on the 12-μF capacitor. The desired charge equals the charge on the equivalent capacitor: (C) Find the voltage drop across the 12-μF capacitor. Apply the basic capacitance equation. 5.0μF 6.0μF 12µF H c=2 1 1 1 1 + 3.0 UF 6.0 μF 12 μF 24 UF 1.6 μF QCqAV (1.6 x 106 F) (18 V) 29 μC → AV- Av. 18 V Ο 29 με 12 UF 24 μF = 2.4 V LEARN MORE REMARKS Notice that the equivalent capacitance is less than that of any of the individual capacitors. The relationship C Q/AV can be used to find the voltage drops on the other capacitors, just as in part (c). QUESTION Over which capacitor is the voltage drop the smallest? 81322.2 QUESTION Over which capacitor is the voltage drop the smallest? the 3.0-μF capacitor the 6.0-μF capacitor the 12-μF capacitor the 24-µF capacitor Over which capacitor is the voltage drop the largest? the 3.0-µF capacitor the 6.0-μF capacitor the 12-µF capacitor O the 24-µF capacitor PRACTICE IT Use the worked example above to help you solve this problem. Four capacitors are connected in series with a battery, as in the figure below, where C₁ = 3.52 μF, C₂ = 6.57 UF, C3= 13.0 μF, C4 = 24.7 μF, V 18.8 V. Ci HH C₂ C₂ Ca (a) Calculate the capacitance of the equivalent capacitor. 1.45 (b) Compute the charge on C3- μC X Your response differs from the correct answer by more than 10%. Double check your calculations. UF = = (a) Calculate the capacitance of the equivalent capacitor. 1.45 X (b) Compute the charge on C3. μc = Your response differs from the correct answer by more than 10%. Double check your calculations. UF (c) Find the voltage drop across C3. V EXERCISE HINTS: GETTING STARTED I I'M STUCK! Use the values from PRACTICE IT to help you work this exercise. C4 is removed from the circuit, leaving only three capacitors in series. (a) Find the equivalent capacitance. Ceq = UF = (b) Find the charge on C₂. Q = μC (c) Find the voltage drop across C₂- AV = V
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Fundamentals of Ethics for Scientists and Engineers
ISBN: 978-0195134889
1st Edition
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F12-17 Find [v] and a when t=0.5s. y X = = (41) m 4x X
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In a one-dimensional flat wall with a thickness of 1 and a coefficient of thermal conductivity k. steady- state thermal conductivity takes place, in which the temperature of the wall is a function...
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69. A model pump with a 40-cm-diameter impeller requires a 9-kW power input when operating at a speed of 1500 rpm against a head of 7.5 m. A homologous pump 1.9 m in diameter will operate at the same...
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Your Company had a beginning balance in its Accounts Receivable of $250,000. Your Company earned $850,000 of revenue on account during the current year. It also had $600,000 of cash sales. Your...
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Revol Industries manufactures plastic bottles for the food industry. On average, Revol pays $76 per ton for its plastics. Revol's waste-disposal company has increased its waste-disposal charge to $57...
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What is the approximate average velocity of the race cars during the Indianapolis 500?
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Give examples in which the directions of the velocity and position vectors are (a) Opposite, (b) The same, (c) Mutually perpendicular.
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The density of aluminum is 2.7 g/cm3. How many free electrons are present per aluminum atom?
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Use Table 15.1 to find the short rate in the fourth year. Confirm that the discount factor on the 4-year zero is a geometric average of 1 + the short rates in the next four years. Table 15.1...
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Using the data in Table 15.1, calculate the price and yield to maturity of a 3-year bond with a coupon rate of 4% making annual coupon payments. Does its yield match that of either the 3-year zero or...
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Suppose that the required liquidity premium for the short-term investor is 1%. What must E(r2) be if f2 is 7%?
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