אנרגיה חשמלית במעגלי קבלים - בעיות ופתרונות
1. לקבוע את אנרגיה חשמלית במעגל המוצג באיור למטה (1 מיקרופרנהייט = 10-6 F)
ידוע:
קבל 1 (ג1) = 3 מיקרופרנהאט 
קבל 2 (C2) = 1 מיקרופרנהאט
קבל 3 (C3) = 2 מיקרופרנהאט
קבל 4 (C4) = 6 מיקרופרנהאט
קבל 5 (C5) = 4 מיקרופרנהאט
מתח חשמלי (V) = 5 וולט
מבוקש: Electrical energy in circuits
פתרון:
הקבל המקביל:
Capacitor 2 and capacitor 3 are connected in parallelהקבל המקביל:
CA = C2 + ג3 = 1 + 2 = 3 מיקרופרנהאט
Capacitor 1, capacitor A and capacitor 4 are connected in seriesהקבל המקביל:
1 / CB = 1/C1 + 1/CA + 1/C4 = 1/3 + 1/3 + 1/6 = 2/6 + 2/6 + 1/6 = 5/6
CB = 6/5 µF
Capacitor B and capacitor 5 are connected in parallel. The equivalent capacitor :
ג = גB + ג5 = 6/5 + 4 = 6/5 + 16/4 = 24/20 + 80/20 = 104/20 = 5.2 µF
C = 5.2 x 10-6 פאראד
Electrical energy in circuit :
E = ½ C V2 = ½ (5.2 x 10-6)(52) = (2.6 x 10-6)(25)
E = 65 x 10-6 ג'אוּל
2. קבע את electrical energy in capacitor circuits shown in figure below (1 µF = 10-6 F)
ידוע:
קבל 1 (C1) = 4 מיקרופרנהאט 
קבל 2 (C2) = 6 מיקרופרנהאט
קבל 3 (C3) = 12 מיקרופרנהאט
קבל 4 (C4) = 2 מיקרופרנהאט
קבל 5 (C5) = 2 מיקרופרנהאט
Electric voltage (V) = 40 volts
מבוקש: Electrical energy in circuits
פתרון:
הקבל המקביל:
Capacitor 1, capacitor 2 and capacitor 3 are connected in series. The equivalent capacitor :
1 / CA = 1/C1 + 1/C2 + 1/C3 = 1/4 + 1/6 + 1/12 = 3/12 + 2/12 + 1/12 = 6/12
CA = 12/6 = 2 מיקרופרנהאט
Capacitor 4 and capacitor 5 are connected in series. The equivalent capacitor :
1 / CB = 1/C4 + 1/C5 = 1/2 + 1/2 = 2/2
CB = 2/2 = 1 מיקרופרנהאט
Capacitor A and capacitor B in parallel. The equivalent capacitor :
ג = גA + גB = 2 + 1 = 3 מיקרופרנהאט
C = 3 x 10-6 פאראד
Electrical energy in circuits :
E = ½ C V2 = ½ (3 x 10-6)(402) = (1.5 x 10-6)(1600)
E = 2400 x 10-6 = 2.4 x 10-3 ג'אוּל
3. Determine the energy stored in the electrical circuit shown in the figure below.
ידוע:
קבל 1 (C1) = 4 פ 
קבל 2 (C2) = 4 פ
קבל 3 (C3) = 4 פ
קבל 4 (C4) = 4 פ
קבל 5 (C5) = 2 פ
Electric voltage (V) = 12 volts
מבוקש: Electrical energy in circuits
פתרון:
הקבל המקביל:
Capacitor 1, capacitor 2 and capacitor 3 are connected in parallel. The equivalent capacitor :
CA = C1 + ג2 + ג3 = 4 + 4 + 4 = 12 F
Capacitor 4 and capacitor 5 are connected in parallel. The equivalent capacitor :
CB = C4 + ג5 = 4 + 2 = 6 F
Capacitor A and capacitor B are connected in series. The equivalent capacitor :
1/C = 1/CA + 1/CB = 1/12 + 1/6 = 1/12 + 2/12 = 3/12
C = 12/3 = 4 פאראד
Electrical energy in circuits :
E = ½ C V2 = ½ (4)(122) = (2)(144)
E = 288 Joule
1. שאלה: How is energy stored in a capacitor?
תשובה: Energy in a capacitor is stored in the electric field between its plates. When a voltage is applied across a capacitor, positive charges accumulate on one plate and negative charges on the opposite plate, creating an electric field.
2. שאלה: What is the formula for the energy stored in a capacitor?
תשובה: The energy (U) stored in a capacitor is given by �=12��2 where C is the capacitance and V is the voltage across the capacitor.
3. שאלה: What happens to the energy stored in a capacitor when the voltage is doubled?
תשובה: Since the energy is proportional to the square of the voltage (V^2), when the voltage is doubled, the energy increases by a factor of four.
4. שאלה: Why can a charged capacitor be dangerous even if it’s disconnected from its voltage source?
תשובה: A charged capacitor can retain its stored energy even when disconnected from its voltage source. If a conductor (or a person) comes into contact with the terminals, the stored energy can be rapidly released, potentially causing harm or damage.
5. שאלה: How does the energy stored in a capacitor change if the capacitance is halved while keeping the voltage constant?
תשובה: If the capacitance is halved and voltage remains constant, the energy stored will also be halved, as the energy is directly proportional to the capacitance.
6. שאלה: What role does the dielectric material play in a capacitor?
תשובה: The dielectric material increases the capacitance of the capacitor by reducing the effective electric field between the plates and also prevents charge conduction between the plates.
7. שאלה: In a series capacitor circuit, how does the total capacitance compare to the individual capacitances?
תשובה: In a series arrangement, the inverse of the total capacitance (1/C_total) is the sum of the inverses of the individual capacitances. This means the total capacitance in a series configuration is always less than the smallest capacitance in the series.
8. שאלה: How is the total capacitance calculated for capacitors connected in parallel?
תשובה: For capacitors in parallel, the total capacitance is the sum of the individual capacitances.
9. שאלה: Why does a capacitor block direct current (DC) but allow alternating current (AC) to pass through?
תשובה: A capacitor blocks DC because once it’s fully charged, no further current can flow. However, with AC, the voltage is continuously changing, causing the capacitor to charge and discharge, allowing an effective current to flow.
10. שאלה: What happens to a capacitor’s voltage if it is connected to a battery and then disconnected before reaching full charge?
תשובה: The capacitor will retain the voltage it had at the moment of disconnection and won’t charge further unless connected back to a power source.
