Electrostatic Energy & Capacitors
1. A parallel-plate capacitor has a plate area of 0.2 m2 and a plate separation of 0.1
mm. To obtain an electric field of 2.0 106 V/m between the plates, the magnitude of
the charge on each plate should be:
A) 8.9 10ˉ7C
B) 1.8 10ˉ6C
C) 3.5 10ˉ6C
D) 7.1 10ˉ6C
E) 1.4 10ˉ5C
A
Solutions: Q VC E d 0 E 0 A 2 106 1011 0.2 4 106 C
d
Ans: C
1 . A parallel-plate capacitor has a plate area of 0.2 m2 and a plate separation of 0.1
mm. If the charge on each plate has a magnitude of 4 10–6 C the potential difference
across the plates is approximately:
A) 0
B) 4 10–2 V
C) 1 102 V
D) 2 102 V
E) 4 108 V
Q Q d 4 106 0.1 103
Solutions: V 2 102V
C 0 A 11
10 0.2
Ans: D
1 . Two conducting spheres have radii of R1 and R2 with R1 greater than R2. If they
are far apart the capacitance is proportional to:
A) R1R2/(R1 +R2)
B) R1R2/(R1 – R2)
C) (R1+ R2)/R1R2
D) (R1 – R2)/R1R2
E) none of these
, Q
Solutions: For isolated spheres: V
4 0 R
1 Q2 Q1
V2 V1
4 0 R2 R1
Q 1 1 Q
Setting Q2 Q Q1 , we have V V2 V1
4 0 R2 R1 C
R1R2
C 4 0
R1 R2
Ans: A
2. A 2-F and a 1-F capacitor are connected in parallel and a potential difference
is applied across the combination. The 2-F capacitor has:
A) twice the charge of the 1-F capacitor
B) half the charge of the 1-F capacitor
C) twice the potential difference of the 1-F capacitor
D) half the potential difference of the 1-F capacitor
E) none of the above
Q Q1 Q2 2
Solutions: V Q2 Q1 2Q1
C C1 C2 1
Ans: A
3. Two identical capacitors are connected in series and two, each identical to the
first, are connected in parallel. The equivalent capacitance of the series connection is
________ the equivalent capacitance of parallel connection.
A) twice
B) four times
C) half
D) one fourth
E) the same as
1 1
Solutions: Cseries C C parallel C C 2C
1 1 2
C C
Ans: D
1. A parallel-plate capacitor has a plate area of 0.2 m2 and a plate separation of 0.1
mm. To obtain an electric field of 2.0 106 V/m between the plates, the magnitude of
the charge on each plate should be:
A) 8.9 10ˉ7C
B) 1.8 10ˉ6C
C) 3.5 10ˉ6C
D) 7.1 10ˉ6C
E) 1.4 10ˉ5C
A
Solutions: Q VC E d 0 E 0 A 2 106 1011 0.2 4 106 C
d
Ans: C
1 . A parallel-plate capacitor has a plate area of 0.2 m2 and a plate separation of 0.1
mm. If the charge on each plate has a magnitude of 4 10–6 C the potential difference
across the plates is approximately:
A) 0
B) 4 10–2 V
C) 1 102 V
D) 2 102 V
E) 4 108 V
Q Q d 4 106 0.1 103
Solutions: V 2 102V
C 0 A 11
10 0.2
Ans: D
1 . Two conducting spheres have radii of R1 and R2 with R1 greater than R2. If they
are far apart the capacitance is proportional to:
A) R1R2/(R1 +R2)
B) R1R2/(R1 – R2)
C) (R1+ R2)/R1R2
D) (R1 – R2)/R1R2
E) none of these
, Q
Solutions: For isolated spheres: V
4 0 R
1 Q2 Q1
V2 V1
4 0 R2 R1
Q 1 1 Q
Setting Q2 Q Q1 , we have V V2 V1
4 0 R2 R1 C
R1R2
C 4 0
R1 R2
Ans: A
2. A 2-F and a 1-F capacitor are connected in parallel and a potential difference
is applied across the combination. The 2-F capacitor has:
A) twice the charge of the 1-F capacitor
B) half the charge of the 1-F capacitor
C) twice the potential difference of the 1-F capacitor
D) half the potential difference of the 1-F capacitor
E) none of the above
Q Q1 Q2 2
Solutions: V Q2 Q1 2Q1
C C1 C2 1
Ans: A
3. Two identical capacitors are connected in series and two, each identical to the
first, are connected in parallel. The equivalent capacitance of the series connection is
________ the equivalent capacitance of parallel connection.
A) twice
B) four times
C) half
D) one fourth
E) the same as
1 1
Solutions: Cseries C C parallel C C 2C
1 1 2
C C
Ans: D
