วงจรตัวเก็บประจุแบบอนุกรมและแบบขนาน – ปัญหาและวิธีแก้ไข
1. What is the total โหลด ที่ capacitor circuits below (1 μF = 10-6 F)
เป็นที่รู้จัก :
ตัวเก็บประจุ 1 (C1) = 3 μF
ตัวเก็บประจุ 2 (C2) = 3 μF
ตัวเก็บประจุ 3 (C3) = 3 μF
ตัวเก็บประจุ 4 (C4) = 2 μF
ตัวเก็บประจุ 5 (C5) = 3 μF
แรงดันไฟฟ้า (V) = 3 โวลต์
เป็นที่ต้องการ : Total charge in capacitor circuits (Q)
วิธีการแก้ปัญหา:
The equivalent capacitor
ตัวเก็บประจุ C1,2 และ C3 are connected in series. The equivalent capacitor :
1 / C123 = 1/C1 + 1/C2 + 1/C3 = 1/3 + 1/3 + 1/3 = 3/3
C123 = 3/3 = 1 μF
ตัวเก็บประจุ C123 และ C4 are connected in parallel. The equivalent capacitor :
C1234 = C123 + C4 = 1 + 2 = 3 μF
ตัวเก็บประจุ C1234 และ C5 are connected in series. The equivalent capacitor :
1/C = 1/C1234 + 1/C5 = 1/3 + 1/3 = 2/3
C = 3/2 μF
C = 3/2 x 10-6 F
The total charges :
The total charges in the equivalent capacitor = the total charges in capacitor circuits :
Q = V C = (3 Volt)(3/2 x 10-6 Farad) = 9/2 x 10-6 คูลอมบ์
Q = 9/2 microCoulomb = 9/2 μC
Q = 4.5 μC
2. If C1 = C2 = 2 μF, C3 = C4 = 1 μF and C5 = 4 μF, determine the total charges in the capacitor circuits as shown in figure below (1 μF = 10-6 F)
เป็นที่รู้จัก :
ตัวเก็บประจุ 1 (C1) = 2 μF
ตัวเก็บประจุ 2 (C2) = 2 μF
ตัวเก็บประจุ 3 (C3) = 1 μF
ตัวเก็บประจุ 4 (C4) = 1 μF
ตัวเก็บประจุ 5 (C5) = 4 μF
แรงดันไฟฟ้า (V) = 1.5 โวลต์
เป็นที่ต้องการ : The total charges in circuits (Q)
วิธีการแก้ปัญหา:
The equivalent capacitor :
ตัวเก็บประจุ C3 และ C4 are connected in parallel. The equivalent capacitor :
C34 = C3 + C4 = 1 + 1 = 2 μF
ตัวเก็บประจุ C5,1,2 และ C34 are connected in series. The equivalent capacitor :
1/C = 1/C5 + 1/C1 + 1/C2 + 1/C34
1/C = 1/4 + 1/2 + 1/2 + 1/2
1/C = 1/4 + 2/4 + 2/4 + 2/4
1/C = 7/4
C = 4/7 μF
C = 4/7 x 10-6 F
The total charges :
The total charges in the equivalent capacitor = the total charges in capacitor circuits :
Q = V C = (1.5 Volt)(4/7 x 10-6 Farad) = 6/7 x 10-6 คูลอมบ์
Q = 6/7 microCoulomb
Q = 6/7 μC
3. Determine the total charges in the capacitor circuits as shown in figure below.
เป็นที่รู้จัก :
ตัวเก็บประจุ 1 (C1) = 3 μF
ตัวเก็บประจุ 2 (C2) = 3 μF
ตัวเก็บประจุ 3 (C3) = 4 μF
ตัวเก็บประจุ 4 (C4) = 4 μF
ตัวเก็บประจุ 5 (C5) = 8 μF
แรงดันไฟฟ้า (V) = 10 โวลต์
เป็นที่ต้องการ : The total charge in the circuits (Q)
วิธีการแก้ปัญหา:
The equivalent capacitor :
ตัวเก็บประจุ C1 และ C2 are connected in parallel. The equivalent capacitor :
C12 = C1 + C2 = 3 + 3 = 6 μF
ตัวเก็บประจุ C3 และ C4 are connected in series. The equivalent capacitor :
1 / C34 = 1/C3 + 1/C4 = 1/4 + 1/4 = 2/4
C34 = 4/2 = 2 μF
ตัวเก็บประจุ C12, ตัวเก็บประจุ C34 and capacitor C5 are connected in parallel. The equivalent capacitor :
ซี = ซี12 + C34 + C5 = 6 + 2 + 8 = 16 μF = 16 x 10-6 หน่วยวัดความจุไฟฟ้าใน
The total electric charges :
The total charges in the equivalent capacitor = the total charges in capacitor circuits :
Q = V C = (10 Volt)(16 x 10-6 Farad) = 160 x 10-6 คูลอมบ์
Q = 160 microCoulomb = 160 μC
20 conceptual questions and answers related to series and parallel capacitors circuits:
1. คำถาม: How are capacitors connected in a series configuration?
คำตอบ: In a series configuration, capacitors are connected end-to-end, so the same current flows through all capacitors.
2. คำถาม: How are capacitors connected in a parallel configuration?
คำตอบ: In a parallel configuration, capacitors are connected across common points or junctions, allowing different currents through each capacitor but maintaining the same voltage across them.
3. คำถาม: How do you calculate the equivalent capacitance for capacitors in series?
คำตอบ: The reciprocal of the equivalent capacitance in a series connection is the sum of the reciprocals of individual capacitances: 1/Cₑq = 1/C₁ + 1/C₂ + … + 1/Cₙ.
4. คำถาม: How do you calculate the equivalent capacitance for capacitors in parallel?
คำตอบ: The equivalent capacitance in a parallel connection is the sum of individual capacitances: Cₑq = C₁ + C₂ + … + Cₙ.
5. คำถาม: What happens to the total capacitance when capacitors are added in series?
คำตอบ: Adding capacitors in series decreases the total or equivalent capacitance.
6. คำถาม: What happens to the total capacitance when capacitors are added in parallel?
คำตอบ: Adding capacitors in parallel increases the total or equivalent capacitance.
7. คำถาม: How is the charge stored on capacitors connected in series?
คำตอบ: The charge stored on each capacitor in a series connection is the same because the same current flows through all of them.
8. คำถาม: How is the voltage distributed across capacitors connected in series?
คำตอบ: The total voltage is divided among the capacitors in series, and the voltage across each capacitor is inversely proportional to its capacitance.
9. คำถาม: How does the energy stored in a series or parallel combination of capacitors compare to the energy stored in individual capacitors?
คำตอบ: The total energy stored in a combination of capacitors is the sum of the energy stored in individual capacitors, regardless of whether they are in series or parallel.
10. คำถาม: How does the breakdown voltage of a series combination of capacitors compare to individual capacitors?
คำตอบ: In a series combination, the breakdown voltage is typically determined by the capacitor with the lowest breakdown voltage.
11. คำถาม: What is the importance of using capacitors with the same voltage rating in a parallel configuration?
คำตอบ: Using capacitors with the same voltage rating in parallel ensures that each capacitor can handle the common voltage across them, preventing potential damage or failure.
12. คำถาม: Why might you use capacitors in series?
คำตอบ: Capacitors in series can be used to achieve a lower equivalent capacitance or to increase the overall breakdown voltage of the combination.
13. คำถาม: Why might you use capacitors in parallel?
คำตอบ: Capacitors in parallel can be used to increase the total capacitance or to distribute the charge storage across multiple capacitors for applications requiring high charge capacity.
14. คำถาม: How can the total energy stored in a parallel combination of capacitors be calculated?
คำตอบ: The total energy can be calculated as ½ Cₑq V², where Cₑq is the equivalent parallel capacitance, and V is the common voltage.
15. คำถาม: What is the effect of having unequal capacitances in a series connection?
คำตอบ: In a series connection with unequal capacitances, the voltage distribution will vary, with smaller capacitors having a larger voltage drop across them.
16. คำถาม: How can capacitors in series and parallel be utilized in tuning circuits?
คำตอบ: Series and parallel configurations of capacitors can be used to achieve specific resonant frequencies or phase shifts in tuning circuits, such as in radios or signal processing.
17. คำถาม: What could happen to the equivalent capacitance of a parallel combination if one capacitor fails short-circuited?
คำตอบ: A short-circuited capacitor in parallel would effectively be removed from the circuit, leading to a decrease in the equivalent capacitance.
18. คำถาม: What could happen to the equivalent capacitance of a series combination if one capacitor fails open-circuited?
คำตอบ: An open-circuited capacitor in a series would break the current flow, making the equivalent capacitance zero.
19. คำถาม: How do series and parallel combinations of capacitors affect the impedance in AC circuits?
คำตอบ: Series combinations increase impedance, while parallel combinations decrease it. This behavior can be used to filter or pass specific frequencies in AC circuits.
20. คำถาม: Can you mix series and parallel configurations in the same circuit?
คำตอบ: Yes, series and parallel configurations can be mixed within the same circuit to achieve desired capacitance values and characteristics. The analysis requires applying the rules for both series and parallel combinations.
Understanding the properties and behaviors of capacitors in series and parallel configurations is vital in the design and analysis of electronic circuits, allowing engineers to tailor circuits to specific needs and functions.
