METU D. F. HIGH SCHOOL ACADEMIC YEAR

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Dortha Scott
7 years ago
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1 A capacitor is connected to the terminals of a battery as shown in the figure. A capacitor is charged and disconnected from the battery as shown in the figure. After a dielectric is inserted between the plates of capacitor; After a dielectric is inserted between the plates of capacitor; a) The capacitance of capacitor. b) Potential difference across the plates. increases increases c) Charge of capacitor. remains the same increases a) The capacitance of capacitor.. b) Potential difference across the plates. remains the same c) Charge of capacitor. decreases decreases d) The electric field between the plates. remains the same d) The electric field between the plates.

2 Two capacitors are arranged as shown. The capacitor C 1 has a charge of 20µC and the capacitor C 2 is uncharged. The switches S 1 and S 2 are closed at the same time. Calculate; a) final charges of each capacitor. b) the potential difference across the plates of each capacitor. c) the energy stored in the capacitor C 1. a) Q total =20 µc Q / 1=5 µc and Q / 2=15 µc For the circuit given calculate a) Equivalent capacitance of the system b) Total charge of the system c) The charge of the each capacitor d) Potential difference across the plates of each capacitor. a) C eq =2 µf b) Q total =24 µc b) V=5/3 volts c) Q 1 = Q 2 =24 µc c) E=(CV 2 )/2=(3.(5/3) 2 )/2=25/6 µj d) V 1 =8 V and V 2 =4 V

3 The potential difference across the plates of C 1 is 40 volts. 6. After the capacitors are fully charged an insulator with K=2 is inserted between the plates of C 1 and the system is again fully charged. Calculate; a) The potential difference of C 2 b) The potential difference of battery c) The total charge of system a) Q 1 = Q 2 =120 C then V 2 =(120)/(6)=20 V b) V=40+20=60 V a) What is change in the charge of C 1? b) What is change in the potential of C 1? a) C eq = 2 F Q 1 = Q 2 =12 C then After dielectric is inserted; C / 1=6 F then C / eq= 3 F Q / 1= Q / 2=18 C c) C eq = 2 F and V=60 V Q total =2.60=120 C b) V 1 =4 V and V 2 =8 V After dielectric is inserted; V / 1=3 V and V / 2=3 V

4 7. 8. After the capacitors are fully charged an insulator having a dielectric constant K=2 is inserted between the plates of C 1 and the system is again fully charged. For the given circuit, calculate a) The equivalent capacitance and the total charge of the system. c) The potential difference across each capacitor. d) The charge stored on each capacitor. e) The electric potential energy of the system. a) C eq = 1+2=3 µf Q total = 12.3 =36 µc b) V 1 = V 2 =12 V c) Q 1 = 1.12 =12 µc Q 2 = 2.12 =24 µc d) E total =CV 2 /2=( )/2 E total =216 µj a) What is change in the charge of C 1? b) What is change in the potential of C 1? c) How does the charge of C 2 change? Why? a) Q 1 = 3.12=36 µc C 1 = 3 µf then C / 1= 6 µf (with dielectric) Q / 1= 6.12=72 µc b) V 1 = V / 1=12 V c) Q 2 = Q / 2=48 µc

5 When the switches S 1 and S 2 are open, the equivalent capacitance of the circuit is 6 µf. For the circuit given, Calculate a) charge stored on each capacitor b) potential difference across each capacitor c) energy stored in C 2 a) 2 F and 4 F are parallel : 6 F 6 F and 12 F are series : C eq = 4 µf then Q total =4.12=48 µc Q 1 =48 µc, Q 2 =16 µc and Q 3 =32 µc b) V 1 =4 V and V 2 =V 3 =8 V c) E 2 =(2.8 2 )/2=64 J What is the equivalent capacitance of the circuit when both switches are closed? When both switches are open C eq =C=6 µf When both switches are closed C eq =10C/3 C eq =(10.6)/3=20 µf

6 When the switch S is open the total charge of the system is Q 1. When the switch is closed the total charge of the system becomes Q 2. Calculate the ratio of Q 1 / Q 2? Calculate the equivalent capacitance between points K and L. S is open; 4 F and 4 F are series C eq =2 F then Q 1 =2.V Q 1 /Q 2 =(2.V)/(8.v/3) Q 1 /Q 2 =3/4 S is closed; 4 F and 4 F are paralle:8 F C eq =8/3 F then Q 2 =8.V/3 C eq = C eq =20 F

7 A 40 µf capacitor is charged by connecting it to 16 V battery. The battery is then disconnected and the charged capacitor is next connected across a 120 µf that was initially uncharged. After steady state has been reached, what is the charge on each capacitor and the voltage across each? If the potential difference between the ends of 3µF capacitor is 24 V, what is the potential difference between points K and L? Initially; Q i =40.16=640 µc 6.V=3.24 V=12 V V KL =12+24 V KL =36 V then Q total =640 µc Q 1 =160 µc and Q 2 =480 µc (Q is directly proportional to C when two capacitors are parallel.) V common =160/40=4 V

8 The potential difference between the two ends of 12 µf capacitor is 40 V. What is the equivalent capacitance between the points K and L? What is the amount of charge stored in the 6µF capacitor, in µc? 12 µf and 3 µf : parallel: 15 µf 6 µf and 4 µf : parallel: 10 µf 8 F and 24 F : series : 6 F 6 F and 18 : parallel : 24 F 24 F and 12 F : series : C eq =8 F 10 µf and 15 µf : series Their charges are the same =V.10 then V=60 V The charge on 6 µf capacitor is Q=6.60=360 µc

Q24.1 The two conductors a and b are insulated from each other, forming a capacitor. You increase the charge on a to +2Q and increase the charge on b

Q24.1 The two conductors a and b are insulated from each other, forming a capacitor. You increase the charge on a to +2Q and increase the charge on b to 2Q, while keeping the conductors in the same positions.