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